Problema Solution
Jim drove to Portland, a distance of 300 miles. during the last 80 miles of the trip, heavy rain forced him to decrease his speed by 15 mph. if his total drive time was 6 hours, find his original speed and his speed during the rain.
Answer provided by our tutors
Let
v = the original speed, v>=0
v - 15 = the speed during rain, v - 15 >=0, v >= 15
The first 300 - 80 = 220 miles Jim drove with a speed of v miles per hour thus the time of the travel of this distance was: 220/v (since time = distance/speed).
The last 80 miles of the trip Jim's speed decreased to v - 15 and the time that he traveled the last 80 miles was: 80/(v - 15)
We know that the total time of the trip was 6 hours:
220/v + 80/(v - 15) = 6
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click here to see the equation solved for v
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v = 55 mph
We need to ignore the solution 10 mph because v - 15 = 10 - 15 = -5 < 0 that is the speed of the truck for the last 80 miles of the road can not be negative.
v - 15 = 55 - 15 = 40 mph
The original speed of the truck was 55 mph.
The speed during rain was 40 mph.