Question

Roma Sherry drove 60 miles from her home town to her​ parents' town. During her return​ trip, she was able to increase her speed by 33 miles per hour. If her return trip took 1 hour less​ time, find her original speed and her speed returning home. What should be done first?

A. Interpret the solution.
B. Translate the problem into an equation.
C. Choose a variable to represent the unknown.
The key idea here is the relationship between the time, rate and distance. Let x be the orignal speed. Then the retum-rip speed is:______.

Answer 1

The correct answer is 63.93 miles per hours.

Explanation:

Let Roma's speed while going to to her parents' town is x miles per hour. And the time taken by her be k hours.

Return speed is x + 33 miles per hour. Time taken is k - 1 hours.

Distance between Roma's house and her parents is 60 miles.

Therefore the problem can be written in equation as kx = (x + 33) (k - 1) = 60

⇒ 60 + 33
`k^(2)` - 33k - 60k = 0

⇒ 11
`k^(2)` - 11 k - 20 = 0

⇒ k = 11 ± √1001 ×
`(1)/(22)` = 1.94 and -0.94.

Thus the value of k is 1.94 hour and the value of x is 30.93 mile per hour.

Return speed is 63.93 miles per hour.