Question

6. Alex and Brian park their bikes side-by-side. Alex leaves to visit friends, and Brian leaves 30 minutes later,

headed for the same destination. Alex pedals 5 miles per hour slower than Brian. After 1 hour, Brian passes Alex. At
what speed are they each pedaling?

Answer 1

See below.

Explanation:

When Brian passes Alex they both have travelled the same distance.

Call this distance d.

Let the speed that Brian passes = x miles/hour.

Distance = speed * time so:

For Alex:

d = (x - 5) * 1.5 ( Alex cycles for 1 + 30 minutes = 1.5 hours)

For Brian:

d = x * 1

So substituting d = x in Alex's equation:

x = 1.5(x - 5)

x = 1.5x - 7.5

7.5 = 0.5x

7/5 / 0.5 = x

15 = x.

ANSWER:

Brian's speed is 15 miles/hour.

Alex's speed is 15 - 5 = 10 miles/hour.