Answer:
The correct answer is 63.93 miles per hours.
Step-by-step 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 [tex]k^{2}[/tex] - 33k - 60k = 0
⇒ 11[tex]k^{2}[/tex] - 11 k - 20 = 0
⇒ k = 11 ± √1001 × [tex]\frac{1}{22}[/tex] = 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.
