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

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

Step-by-step 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=(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=((S)/(2))/(65)+((S)/(2))/(45)=(S)/(130)+(S)/(90)=(220S)/(130* 90)=(11S)/(585)`

Ratio of time of arrival of B to A

`(t_B)/(t_A)=((11S)/(585))/((S)/(55))=(121)/(117)=1.034`

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