Aaron travels from town X to town Y and then back from town Y to town X, taking different routes in each direction. If his speed when travelling from town X to town Y is 36 miles per hour, and his speed when travelling in the opposite direction is 48 miles per hour, what is his average speed for the entire journey?
1) The length of the return trip is 24% of the entire distance traveled.
2) The length of the return trip is 100 miles.
Amy reached from her home to her aunt’s place in 75 minutes. What is the average speed at which Amy drove her car?
(1) She travelled the first 30 minutes at 60 miles per hour and remaining at 80 miles per hour.
(2) The total distance between Amy and her aunt’s home is 90 miles.
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A ferry crosses a lake and then returns to its starting point by the same route. The first time it crosses the lake, the ferry travels at 15 kilometers per hour. The ferry’s return trip takes 3 hours. How many hours does the ferry take for the first leg of the trip?
(1) The ferry’s average speed for the entire round trip is 12 kilometers per hour.
(2) The distance the ferry covers to cross the lake once is 30 kilometers.
In an endurance race, a car drove the whole race at a constant speed of 3 miles per minute to cover the total race distance D. Was the value of D greater than 500 miles?
Statement 1. The time taken by the car to cover D was more than 2 hours.
Statement 2. The time taken by the car to cover D was less than 2.75 hours.
Bob ran a 20-mile race. At what time did he finish the race?
1. He started the race at 8:05 am and his average speed for the first 10 miles of the race was 8 miles per hour.
2. He ran at a constant rate and had completed half of the amount of running time at 9:20 AM and had completed 80% of the running time at 10:05 AM.
Today, Samson’s Train traveled at a constant rate along a straight North-South route that included the famous 10-mile long Chasm Bridge. Was Samson’s Train on the Chasm Bridge at 2:00 p.m.?
(1) At 9:00 a.m., Samson’s Train was 200 miles north of the Chasm Bridge, and at 4:00 p.m, the train was 140 miles south of Chasm Bridge.
(2) Samson’s Train started its trip at 6:00 a.m., and traveled at a rate of less than 70 miles per hour.
Al and Barb shared the driving on a certain trip. What fraction of the total distance did Al drive?
(1) Al drove for 3/4 as much time as Barb did.
(2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip.
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?
(1) 2x + 3y = 280
(2) y = x + 10
Tom and Samuel are riding motorcycles down the highway at constant speeds. If Tom is now 2 miles ahead of Samuel, how many minutes before Tom is 3 miles ahead of Samuel?
(1) Tom is traveling at 70 miles per hour and Samuel is traveling at 60 miles per hour.
(2) Tom left 5 minutes before Samuel.
A cyclist rides to the top of a hill and then coasts back down by the same route. The entire trip takes 4 hours. What is his average (arithmetic mean) speed when climbing the hill?
(1) The cyclist's average speed over the entire trip was 6 miles per hour.
(2) The distance to the top of the hill was 12 miles, and the cyclist's average speed on the downward trip was 18 miles per hour.