Question

It took a group of students 5 hours to drive to the beach for Spring Break. On the return home, due to traffic, it took the group 6.5 hours to return home. Their speed was 15 mi/hr slower on their trip home than on drive to the beach. What was their speed on the return trip home?

Answer 1

Answer:

50 mi/hr.

Explanation:

$\begin{gathered} Speed=\frac{Distance}{Time} \\ \implies Distance=Speed\times Time \end{gathered}$

Let the speed on the way to the beach = x mi/hr

The time it took to drive to the beach = 5 hours

$Distance\;covered=5x$

On their trip home, their speed was 15 mi/hr slower.

• Speed = (x-15) mi/hr

The time it took to drive back home = 6.5 hours

$Distance\;covered=6.5(x-15)$

Since the distance to and from the beach is the same, then:

$5x=6.5(x-15)$

We solve the equation for x:

$\begin{gathered} \text{Open the brackets} \\ 5x=6.5x-97.5 \\ \text{ Subtract 6.5x from both sides of the equation.} \\ 5x-6.5x=6.5x-6.5x-97.5 \\ -1.5x=-97.5 \\ \text{ Divide both sides by }-1.5 \\ \frac{-1.5x}{-1.5}=\frac{-97.5}{-1.5} \\ x=65\;\frac{mi}{hr} \end{gathered}$

Thus, the speed on the return home will be:

$x-15=65-15=50\text{ mi/hr}$

Their speed on the return trip home was 50 mi/hr.