Question 1102120
Let s = the speed and t = the time for the first part of the trip
Then s + 9 is the speed for the second part of the trip
The total time is 10 h, so the time for the second leg is 10 - t
For the first leg of the trip s = 258/t -> t = 258/s [1]
For the second leg, s + 9 = 208/(10 - t) [2]
We have two equations and two unknowns
Substitute [1] into [2]:
s + 9 = 208/(10 - 258/s) = 208s/(10s - 258)
(s + 9)(10s - 258) = 208s
10s^2 - 258s + 90s - 2322 - 208s = 0
10s^2 - 376s - 2322 = 0
5s^2 - 188s - 1161 = 0
This gives s = -5.4 and 43. Only the positive solution is valid.
Thus the other speed is 43 + 9 = 52
Ans: 43 mph and 52 mph