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Tavi drives 113 miles at 50 miles per ho...

Tavi drives 113 miles at 50 miles per hour and returns via the same route at 60 miles per hour.
`{:("Quantity A","Quantity B"),("Tavi's average speed for the",55mph),("entire round trip",):}`

A

Quantity A is greater.

B

Quantity B is greater.

C

The two quantities are equal.

D

The relationship cannot be determined from the infromation given.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to calculate Tavi's average speed for the entire round trip and compare it with 55 mph. ### Step-by-Step Solution: 1. **Calculate the time taken for the first leg of the trip (T1)**: - Distance = 113 miles - Speed = 50 mph - Time (T1) = Distance / Speed = 113 miles / 50 mph = 2.26 hours (or 113/50 hours) 2. **Calculate the time taken for the return trip (T2)**: - Distance = 113 miles - Speed = 60 mph - Time (T2) = Distance / Speed = 113 miles / 60 mph = 1.8833 hours (or 113/60 hours) 3. **Calculate the total time for the round trip (T_total)**: - Total Time = T1 + T2 = (113/50) + (113/60) - To add these fractions, find a common denominator. The LCM of 50 and 60 is 300. - Convert T1 and T2: - T1 = (113/50) = (113 * 6) / 300 = 678/300 hours - T2 = (113/60) = (113 * 5) / 300 = 565/300 hours - Total Time = (678/300) + (565/300) = (678 + 565) / 300 = 1243 / 300 hours 4. **Calculate the total distance for the round trip**: - Total Distance = 113 miles (to) + 113 miles (return) = 226 miles 5. **Calculate the average speed for the entire trip**: - Average Speed = Total Distance / Total Time - Average Speed = 226 miles / (1243 / 300) hours - This can be simplified by multiplying by the reciprocal: - Average Speed = 226 * (300 / 1243) = 67800 / 1243 ≈ 54.5 mph 6. **Compare Quantity A and Quantity B**: - Quantity A (Tavi's average speed) = 54.5 mph - Quantity B = 55 mph - Since 54.5 mph < 55 mph, Quantity B is greater than Quantity A. ### Final Answer: - Quantity B is greater than Quantity A.
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