Edwin is planning to drive from Boston to New Orleans. By what percent would his travel time be reduced if Edwin decides

This topic has expert replies
Moderator
Posts: 6595
Joined: 07 Sep 2017
Followed by:20 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Edwin is planning to drive from Boston to New Orleans. By what percent would his travel time be reduced if Edwin decides to split the driving time equally with his friend George, instead of making the trip alone?

(1) The driving distance from Boston to New Orleans is 1500 miles.
(2) George’s driving speed is 1.5 times Edwin’s driving speed.


OA B

Source: Manhattan Prep

Legendary Member
Posts: 2087
Joined: 29 Oct 2017
Followed by:6 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGmoderatorDC wrote:
Wed Mar 02, 2022 4:46 pm
Edwin is planning to drive from Boston to New Orleans. By what percent would his travel time be reduced if Edwin decides to split the driving time equally with his friend George, instead of making the trip alone?

(1) The driving distance from Boston to New Orleans is 1500 miles.
(2) George’s driving speed is 1.5 times Edwin’s driving speed.


OA B

Source: Manhattan Prep
Wanted \(\dfrac{T_{old} - T_{new}}{T_{old}} = ?\)

1) \(D = 1500\). Not sufficient \(\Large{\color{red}\chi}\)

2) Use formula: \(R1T1 + R2T2 = W\)
\(T2 = T1\) (Given: "split the driving time equally")
\(R1 = S\)
\(R2 = 1.5S\)
\(ST1 + 1.5ST1 = D\)
\(T1 (2.5S) = D\)
\(T1 = \dfrac{D}{2.5S}\)

So,
\(T_{new} = T1 + T2 = 2\cdot T1 = \dfrac{2D}{2.5S}\)

Now we have both \(T_{new}\) and \(T_{old}\) so we can stop here. Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, B