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Zeke drove from his house to a furniture store in Atlanta and then back home along the same route. It took Zeke three hours to drive to the store. By driving an average of 20 mph faster on his return trip, Zeke was able to save an hour of driving time. What was Zeke’s average driving speed on his round trip?

A. 24 mph
B. 48 mph
C. 50 mph
D. 60 mph

Answer :

The average speed must be greater than 0 and less than 2D.Therefore, among the given options, the only reasonable choice is c. 50 mph.

Let's use the formula: Distance = Speed × Time to solve this problem.

First, let's denote the following variables:

D = distance to the store (one way)

R = Zeke's regular speed (one way)

F = Zeke's faster speed on the return trip

T1 = time to drive to the store

T2 = time to drive back

We are given that it took Zeke three hours to drive to the store, so T1 = 3 hours.

Now, we are told that by driving an average of 20 mph faster on the return trip, Zeke was able to save an hour of driving time. This means the time he took to return (T2) was one hour less than the time it would have taken him at his regular speed. So, T2 = T1 - 1.

We also know that distance is the same for both legs of the trip, so D = D.

Using the formula Distance = Speed × Time, we can write two equations for the distance to the store:

For the first leg of the trip:

D = R × T1

For the return trip:

D = F × T2

Now, we'll express T2 in terms of T1:

T2 = T1 - 1

We also know that Zeke was able to save an hour, so the difference in time is 1 hour:

T1 - T2 = 1

Substitute T2 from the previous equation into this one:

T1 - (T1 - 1) = 1

Simplify:

T1 - T1 + 1 = 1

1 = 1

This equation is always true, which means there is no inconsistency in the information given. We can solve for T1:

1 hour = 1 hour

Now, let's calculate the average speed for the round trip, which is the total distance divided by the total time:

Average Speed = (2D) / (T1 + T2)

Since T1 = 3 hours and T2 = 2 hours, we can calculate:

Average Speed = (2D) / (3 + 2)

Average Speed = (2D) / 5

Now, let's consider the options:

a. 24 mph

b. 48 mph

c. 50 mph

d. 60 mph

We can't determine the exact value of D from the information given, but we can see that the average speed depends on 2D, which is a positive value, and the denominator is 5. Therefore, the average speed must be greater than 0 and less than 2D.

Given this, we can conclude that the average speed of Zeke's round trip is definitely less than 2D.

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