Question

Hamza lives 35 miles from his office. On the way to work, he drove at his normal speed, but on the way home, traffic caused his driving speed to decrease by 5 miles per hour. The trip home took 2 hours. What was Hamza’s speed on his way to work?
Using the relationship that speed=distance/time, and the information on the return trip, a rational equation that can be used to solve for speed is
. The least common denominator is
, and multiplying both sides by the least common denominator gives an equivalent equation of
. Write the solution to this equation as a decimal:
miles per minute.

Answer 1

The rational equation that can be used to solve for speed is:

35/(x - 5) = 2

In this equation, x represents Hamza's speed on his way to work.

Multiplying both sides of the equation by the least common denominator, which is (x - 5), gives:

35 = 2(x - 5)

35 = 2x - 10

Adding 10 to both sides of the equation gives:

45 = 2x

Dividing both sides of the equation by 2 gives:

x = 22.5

So, Hamza's speed on his way to work was 22.5 miles per hour.

To convert this to miles per minute, we divide by 60 (since there are 60 minutes in an hour):

22.5 miles per hour = 22.5/60 miles per minute = 0.375 miles per minute.