what's the answer?

Question

Hi,

having a hard time with this one.....2 bicyclists, 42 miles apart, begin riding towards each other on a straight street. One cyclist travels at 15 mph, the other at 20 mph. At the same time, Spot (a greyhound dog), starting at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs at 38 mph and turns around instantly  at each cyclist, how far has Spot run when the cyclists meet?

Answer 1

This is a variation of the "Fly between Two Trains."

The distraction is the shape of the Spot's run. Ignore it!

Spot runs the same amount of time that the trains travel (before crashing and smashing Spot, boo hoo).

 

The trains cover 35 mph (15 + 20).

42 mi / 35 mph = 1.2 hr.

 

For Spot

1.2 hr (38 mph) = 45.6 mi