Question

Doug and Carol live787.5 miles apart. They start at the same time and travel toward each other. Doug's speed is7 mph greater than Carol's. If they meet in7.5 hours, find their speeds.

Answer 1

Doug and Carol live 787.5 miles apart.

Distance = 787.5 miles

They start at the same time and travel toward each other.

Doug's speed is 7 mph greater than Carol's.

Let C represents Carol's speed then we can write

D = 7 + C

If they meet in 7.5 hours, find their speeds.

time = 7.5 hours

Recall that the relation between speed, time and distance is given by

$d=s\cdot t$

Let's plug the given values

$787.5=C\cdot7.5+(7+C)7.5$

Where C is Carol's speed, (7 + C) is Doug's speed and 7.5 is the time in hours.

Simplify the equation

$\begin{gathered} 787.5=7.5C+52.5+7.5C \\ 787.5=15C+52.5 \\ 15C=787.5-52.5 \\ 15C=735 \\ C=\frac{735}{15} \\ C=49 \end{gathered}$

So that means Carol's speed is 49 mph

Doug's speed is

D = 7 + 49 = 56 mph

Doug's speed is 56 mph