Greg drove at a constant speed in a rainstorm for 250 miles. He took a break, and the rain stopped He then drove 159 miles at a speed that was 3 miles per hour faster than his previous speed. If he drove for 8 hours, find the car's speed for each part of the trip.

Speed during first part of the trip = 50 miles/hour

Speed during second part of trip  = 53 miles/hour

Step-by-step explanation:

Given:

Distance driven in rainstorm = 250 miles

Distance driven after rain stopped = 159 miles

Speed driven after rain stopped is 3 miles faster than the speed driven in rainstorm.

Total time driven = 8 hours

To find the speed of the car at each part of the trip.

Solution:

There are two parts of the trip.

1) Car driven in rainstorm:

Let the speed of the car during this part in miles/hour be =

Distance covered in this part = 250 miles.

Time taken in this trip =

2) Car driven after rain stopped:

Speed of the car during this part in miles/hour will be =

Distance covered in this part = 159 miles.

Time taken in this trip =

Total time driven can be given as:

Solving for .

Taking LCD.

Simplifying.

Multiplying both sides by

Subtracting both sides by 750.

Subtracting both sides by

Applying quadratic formula.

    and  

∴     and

Since speed cannot be taken as negative, so our solution will be 50 miles per hour.

Speed during first part of the trip = 50 miles/hour

Speed during second part of trip = = 53 miles/hour

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