Answer:
60 miles per hour
Explanation:
Let s represent the speed in miles per hour during the first part of the trip. Then s-10 will be the speed during the last part of the trip.
For speed/time/distance problems, the appropriate relation is the one that is posted on every speed limit sign:
speed = miles/hour = distance/time
Rearranging this relation gives you the expression for time:
time = distance / speed
You are given time and distance and you need to find speed. The time you're given is the total for the two parts of the trip, so ...
4 = 84/s + 130/(s-10) . . . . . . total time = time1 + time2
Multiplying by the product of the denominators, this becomes ...
4s(s-10) = 84(s-10) +130s
4s^2 -254s +840 = 0 . . . . . . subtract the right side to put in standard form
This can be solved using any of several methods for solving quadratic equations. Solutions are ...
s = 60, s = 3.5 . . . . . only the first solution makes any sense in the problem
The speed during the first part of the trip is 60 miles per hour.