For the passenger train: Average speed = 60 km/h Time taken = 50 minutes = 50/60 hours (since 1 hour = 60 minutes) Distance = Speed × Time Distance = 60 km/h × (50/60) hours Distance = 50 km For the cargo train: Average speed = 20 km/h Time taken = The same time as the passenger train, which is 50 minutes = 50/60 hours Distance = Speed × Time Distance = 20 km/h × (50/60) hours Distance = 16.67 km (approx) Since both trains travel the same distance, the distance between stations A and B is 50 km. So, the correct distance between stations A and B is 50 km
Given: Time taken by the pipe to fill the tank = 72 minutes. Time taken with the leak = 72 + 18 = 90 minutes. We have already calculated the rate of the leak to be 1/4 units per minute. Now, to find out how long it will take for the leak to drain a full tank, we need to calculate the time taken to drain 1 tank's worth of water: Time taken = 1 tank / Rate of the leak Time taken = 1 / (1/4) Time taken = 4 minutes Therefore, the correct answer is 4 minutes. This is equivalent to 4/60 = 1/15 hours or approximately 0.067 hours.
The ratio in which the mixtures from jars A and B should be combined to create the new mixture in vessel C with spirit and water in the proportion of 8:5 is indeed 7:9.
Let's find the area of the triangle. Given: Perimeter of the square = 224 cm Let's assume the side length of the square is ""s"" cm. Perimeter of the square = 4 × side length 224 = 4s Now, find the side length ""s"": s = 224 / 4 s = 56 cm The area of the square is given by: Area of square = side length × side length Area of square = 56 cm × 56 cm Area of square = 3136 cm² Since the area of the triangle is half that of the square, the area of the triangle will be: Area of triangle = 3136 cm² / 2 Area of triangle = 1568 cm² Therefore, the area of the triangle is 1568 cm².
To find the circumference of the circular jogging track, we need to use the formula: Circumference = 2 * π * r where ""r"" is the radius of the circle, and ""π"" (pi) is a constant approximately equal to 3.14159. Given: Area of the circular jogging track = 3850 square meters Step 1: Find the radius of the circular jogging track. Area of a circle = π * r^2 3850 = π * r^2 To find ""r,"" divide both sides by π and then take the square root: r^2 = 3850 / π r^2 ≈ 1226.892 r ≈ √1226.892 r ≈ 35 meters (approximately) Step 2: Calculate the circumference using the radius we found. Circumference = 2 * π * r Circumference ≈ 2 * 3.14159 * 35 Circumference ≈ 220 meters (approximately) Therefore, the circumference of the running track is approximately 220 meters.
The idiom or phrase that accurately captures the meaning of "to deliver a direct and accurate message" is: To shoot straight. The phrase "to shoot straight" means to speak or deliver information in a direct, honest, and straightforward manner. It conveys the idea of being honest and not beating around the bush while communicating.
I. I invested some money in savings bonds. II. The aim was to bond the group into closely-knit teams.
Let's reevaluate the solution to verify the distance between points A and B: Given: Boat's speed in still water = 14 kmph Stream's speed = 4 kmph Time taken to cruise downstream from A to B and return to C (located halfway between A and B) = 19 hours Let the distance between points A and B be ""D"" km. When the boat travels downstream (from A to B) with the stream's current, the effective speed is the sum of the boat's speed and the stream's speed: Effective speed downstream = Boat's speed + Stream's speed Effective speed downstream = 14 kmph + 4 kmph Effective speed downstream = 18 kmph Similarly, when the boat travels upstream (from B to C) against the stream's current, the effective speed is the difference between the boat's speed and the stream's speed: Effective speed upstream = Boat's speed - Stream's speed Effective speed upstream = 14 kmph - 4 kmph Effective speed upstream = 10 kmph Given that the boat takes 19 hours to cruise downstream from A to B and return to C (located halfway between A and B), we can set up the following equation based on time, speed, and distance: Time taken downstream + Time taken upstream = Total time D / Effective speed downstream + (D/2) / Effective speed upstream = 19 Now, let's solve for ""D"": D / 18 + (D/2) / 10 = 19 To solve for ""D,"" find the common denominator: 10D + 9D = 19 * 18 * 2 19D = 684 D = 684 / 19 D ≈ 36 km Therefore, the distance between points A and B is approximately 36 km. However, since point C is located halfway between A and B, the total distance between A and B is 2 * 36 km = 72 km. The correct distance between A and B is 72 km, which matches the provided option of 180 km (since the total distance is 2 * 72 km
The elderly man chose to continue occupation till death in a harness rather than live a rusty existence.
I. Mc-Donald's was trying to buy into the newspaper business. II. She will never buy that story about you getting lost.
I. He is determined to get rich quickly. II. This chocolate mousse is too rich for me.
Step 1: After a few days, he discovers that the provisions will be 10 days short, which means he has consumed supplies for 20 days (30 days in February - 10 days short). Step 2: It is predicted that if the remaining provisions are tripled right now, the gap will be made up. So, the remaining provisions after 20 days will be D - 20D/30 = (3/2)D. Step 3: Now, if the remaining supplies are doubled rather than tripled and Darshan's diet is simultaneously reduced by 20%, we get: Remaining supplies = (1 - 20%) * (2) * ((3/2)D) = 0.8 * 2 * ((3/2)D) = 0.8 * 3D = (4/5) * 3D = (12/5)D. Step 4: The original supplies were meant to last for 30 days, but now the remaining supplies (12/5)D will last for (12/5)D / ((3/2)D) = 12/5 * 2/3 = 8/5 days. Step 5: The shortage of days will be 20 days (full month) - 20 days (already consumed) - 8/5 days (remaining supplies) = 92/5 days ≈ 18.4 days. So, the remaining supplies will be insufficient by approximately 18.4 days. The closest option to 18.4 days from the provided choices is 18 days (10 is too low, and 6 is too low). Therefore, the correct answer is 18 days, which is approximately 18.4 days.
I. The fast train to London takes less than an hour. II. Hundreds of prisoners began a fast in protest about prison conditions.
I. My lawyer is going to file a letter of complaint. II. He took a minute or two to compose his thoughts before he replied.
Let's calculate the duration of the full trip. Let the time taken to travel upstream (against the current) be ""t"" hours. Distance covered upstream = 135 km Boat's speed in still water = 12 kmph Current's speed = 3 kmph Speed against the current (upstream) = Boat's speed - Current's speed Speed against the current = 12 kmph - 3 kmph = 9 kmph Distance = Speed × Time 135 km = 9 kmph × t t = 135 km / 9 kmph t = 15 hours Now, the time taken to travel downstream (with the current) will be the same as the time taken upstream because the distance is the same. Total time for the full trip = Time upstream + Time downstream Total time for the full trip = 15 hours + 15 hours Total time for the full trip = 30 hours Therefore, the duration of the full trip in hours is 30 hours. The correct answer is 30 hours.
The original total area of the room is: Original Total Area = Length × Width × Height Original Total Area = (7x) × (3x) × (x) Original Total Area = 21x^3 Now, let's calculate the new dimensions after the given modifications: Length: Halved → New Length = (1/2) × 7x = (7/2) x Width: Doubled → New Width = 2 × 3x = 6x Height: Doubled → New Height = 2 × x = 2x The new total area of the room after the modifications is: New Total Area = New Length × New Width × New Height New Total Area = ((7/2) x) × (6x) × (2x) New Total Area = 42x^3 Now, let's find the percentage increase in the total area: Percentage Increase = ((New Total Area - Original Total Area) / Original Total Area) × 100 Percentage Increase = ((42x^3 - 21x^3) / 21x^3) × 100 Percentage Increase = (21x^3 / 21x^3) × 100 Percentage Increase = 100% So, the percentage of the room's total area that will be added after the given modifications is 100%
