Find the speed of Sarah's car on the first part of the trip.

Question

On a recent trip, Sarah's car traveled 20 mph faster on the first 160 miles than it did on the remaining 80 miles. The total time for the trip was 4 hours. Find the speed of Sarah's car on the first part of the trip.

Answer 1

All you need is the speed-distance formula (speed = distance/time), set up equations for the two parts of the trip, and solve for the unknown variable.

 

First part of the trip

Let's say the speed of the car in the first part of the trip = x mph

Distance = 160 miles

time = distance/speed = 160/x         eq1

 

Second part of the trip

speed = (x-20) mph

distance = 80 miles

time = distance/speed = 80/(x-20)        eq2

 

Now, the total time is given as 4 hours, so we add eq1 and eq2

160/x + 80/(x-20) = 4

 

Which can be solved using quadratic formula (I leave that for you to work it out!) to give:

x = 68.28 mph, or 11.72 mph

Now x = 11.72 mph can not be a solution, because that would mean that the speed in the 2nd part of the trip was 11.72-20 = a negative value, which does not make sense.

Therefore, the only solution is x = 68.28 mph