Matthew Sudak drove 8 miles to pick up his cousin Jack, then drove 11miles to a mall at a speed of 15 mph faster. If Matthew's total travel time was 24 minutes, what was his speed on the trip to pick up Jack?

He drove to pick Jack at a speed of 16.25mph

Step-by-step explanation:

In this question, we are trying to calculate the speed at which Mathew drove to pick up his cousin Jack.

Firstly, we need to calculate some stuffs.

like the total number of distance traveled? That is simply 8 miles + 11 miles = 19 miles! keep this!

Now, we need to know the total average speed. This is the total distance traveled over the time taken. The time taken is 24 minutes, let’s have this in hours. That would be 24/60 = 0.4 hours

The total average speed is thus 19 miles/ 0.4 hours = 47.5 mph

Now let’s go get the speed he drove to Jack!

directly from the question, we were told that the speed to the mall is 15mph faster. This means if the speed he took to fetch Jack was x, the speed to the mall would be x + 15

so this means;

x + x + 15 = 47.5

2x + 15 = 47.5

2x = 32.5

x = 32.5/2

x = 16.25 mph