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