James and George are both cycling on the same road They are

James and George are both cycling on the same road. They are currently 21 miles apart. If the two cyclists bike towards eachother, they will pass each other in 36 minutes. If they cycle in the same direction, James will pass George in 7 hours. Find the average rate if speed, in miles per hour, of both cyclists.

Solution

change 36 min to hrs: 36/60 = .6 hrs
:
let j = J\'s speed
let g = G\'s speed
:
Write a distance equation for each scenario, dist = time * speed
:
.6(j + g) = 21; (towards each other, their speeds are additive)
7(j - g) = 21; (going the same direction, you subtract their speeds)
:
We can simplify both these equations, divide the first by .6, divide the 2nd by 7.
j + g = 35
j - g = 3
-------------adding eliminates g, find j
2j = 38
j = 38/2
j = 19 mph is J\'s speed
:
Use the equation j + g = 35, to find g
19 + g = 35
g = 35 - 19
g = 16 mph is G\'s speed