A jet plane traveling at 500 mph overtakes a propeller plane

A jet plane traveling at 500 mph overtakes a propeller plane traveling at 200mph that had a 2-hour head start. How far from the starting point are the planes? Please help!!Thanks.

Solution

Let x = distance from starting point
:
Write a time equation: time = dist/speed
:
prob time = jet time + 2 hrs
x/200 = x/500 + 2
:
Mult equation by 1000 to get rid of the denominators, resulting in:
5x = 2x + 2(1000)
5x - 2x = 2000
3x = 2000
x = 2000/3
x = 666.67 mi
:
Check using the time:
666.67/ 200 = 3.33 hr
666.67/ 500 = 1.33 hr
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Time differ: = 2 hrs