Jack’s car started from point P toward point Q. At the same time, Jill’s car started at point Q toward point P. They crossed paths (assume there were no crashes) at point R. They continued on their paths, with Jack’s car reaching point Q nine hours after they had crossed paths. Jill’s car reached point P four hours after they had crossed paths. Both cars maintained a constant speed through the journey. Jack’s car maintained 36 mph. What was the speed of Jill’s car, in mph?
+128474 P R Q
324
Note that if it took Jack 9 hrs to go from R to Q....then the distance from Q to R must be 9 * 36 = 324 miles
So.....let T be the time it takes both to reach R
So....Jills Rate (in mph) must be :
[Distance from Q ot R] / [Time to travel from Q to R] = 324 / T
So....the distance that Jack travels must be 36T + 324
And the distance that Jill travels must be 324 + her rate * time to travel from R to P =
324 + (324/ T) * 4
Since these distances are the same, we have this equation :
36T + 324 = 324 + (324/ T) * 4 subtract 324 from both sides
36T = ( 324/T ) * 4
36T = 1296 /T multiply both sides by T
36T^2 =1296 divide both sides by 36
T^2 =36 take the square root of both sides
T = 6 hrs
So Jill's rate must be 324 / 6 = 54 mph
