Find the speed of each truck

Two trucks leave a warehouse at the same time, traveling in opposite directions. The speed of the faster truck is 5 mph faster than the speed of the slower truck. At the end of 5 hours, they are 600 miles apart. Find the speed of each truck.

---

This is a distance, rate, time problem. Distance = rate x time.

Fast truck
distance = d
rate = r + 5 {it is 5 mph faster than the slower truck}
time = 5 {they left at the same time and went for 5 hours}
d = 5(r + 5) {distance = rate x time}

Slow truck
distance = d
rate = r {since the faster truck is r + 5}
time = 5 {they left at the same time and went for 5 hours}
d = 5r {distance = rate x time}

At the end of 5 hours, they are 600 miles apart. In other words, at the end of 5 hours, their combined distances will equal 600. Add the distances together and set equal to 600.

5(r + 5) + 5r = 600 {added the distances together and set equal to 600}
5r + 25 + 5r = 600 {used distributive property}
10r + 25 = 600 {combined like terms}
10r = 575 {subtracted 25 from each side}
r = 57.5 {divided each side by 10}

The rate of the slower truck is 57.5 mph
The rate of the faster truck is 62.5 mph

​Ask Algebra House