For the first 80 mi of a 160mi trip a peron drove 70 mph Wha

For the first 80 mi of a 160-mi trip, a peron drove 70 mph. What speed would he have to travel for the last half of the trip so that the average speed for the entire trip would be 77 mph.

Solution

We know

Speed = Total distance / Time Interval.

Total time = time taken for first 80 miles + time taken for second 80 miles

Time = Total distance/Speed

(160/77) = (80/70) + ( 80/s)

s = speed at second half

(2/77) = (1/70) + (1/s)

2/77 = (s+70)/70s

2(70s) = ( s+70)77

140s = 77s + 5390

63s = 5390

s = 85.56 mph

The speed he have to travel for the last half of the trip is 85.56 mph