Question

While traveling from Boston to Hartford, Person A drives at a constant speed of 55 mph for the entire trip. Person B drives at 65 mph for half the distance and then drives 45 mph for the second half of the distance. When would B arrive in Hartford relative to A? (Assume person A and person B leave Boston at the same time.)

Answer 1

Answer:

B will take 1.034 times the time of A from Boston to Hartford.

Explanation:

Let the distance from Boston to Hartford be S.

Person A drives at a constant speed of 55 mph for the entire trip,

Time taken by person A

             $t_A=\frac{S}{55}$

Person B drives at 65 mph for half the distance and then drives 45 mph for the second half of the distance.

Time taken by person B

            $t_B=\frac{\frac{S}{2}}{65}+\frac{\frac{S}{2}}{45}=\frac{S}{130}+\frac{S}{90}=\frac{220S}{130\times 90}=\frac{11S}{585}$

Ratio of time of arrival of B to A

                      $\frac{t_B}{t_A}=\frac{\frac{11S}{585}}{\frac{S}{55}}=\frac{121}{117}=1.034$

B will take 1.034 times the time of A from Boston to Hartford.