.
Let x be the rate on the first part of the trip, in miles per hour.
Then the rate on the second part was (x+10) mph, according to the condition.
The time to travel the first part was
hours.
The time to travel the second part was
.
The total time is the sum of these partial times, which gives you the "time" equation
+
=
, or
+
=
hours.
To solve the equation, multiply both sides by 3x*(x+10). You will get
63*(x+10) + 63*x = 4x*(x+10).
Simplify it step by step and solve
63x + 630 + 63x = 4x^2 + 40x
4x^2 - 86x - 630 = 0
2x^2 - 43x - 315 = 0
Solve this quadratic equation and take its positive root.
It will be your solution/answer.