Bunuel wrote:

Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles per hour, heading due east at 9 a.m. in one of the trucks. Two hours later Patricia takes off, at 70 miles per hour, in the other truck heading due west. How long from Chuck's departure time will it be until they are 700 miles apart?

A. 3 hrs. 11 minutes

B. 5 hrs.

C. 5 hrs. 50 minutes

D. 7 hrs.

E. 11 hrs. 40 minutes

We can use the following formula:

Distance of Chuck + distance of Patricia = total distance between the trucks

We are given that Chuck leaves the diner at 9 a.m. traveling at a rate of 50 mph and Patricia leaves at 11 a.m. traveling at a rate of 70 mph. We can let Chuck’s time = t + 2 and Patricia’s time = t. Thus, the distance for Chuck is 50(t + 2) = 50t + 100 and the distance for Patricia = 70t. Finally, we have:

50t + 100 + 70t = 700

120t = 600

t = 5

Since Chuck traveled for t + 2 hours, the two trucks were 700 miles apart when Chuck had been driving for 7 hours.

Answer: D

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