BTGModeratorVI wrote: ↑

Sat Mar 21, 2020 9:49 am

Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?

(A) 105
(B) 120
(C) 140
(D) 147
(E) 168

Answer: A
Source: Kaplan

Okay, so when car Y STARTS moving, car X has already traveled 42 miles
So, let's let t = the travel time starting when car Y STARTS moving

So, car X's TOTAL travel distance = 42 + 35t
So, car Y's TOTAL travel distance = 49t

We want the cars' travel distance to be EQUAL.
We can write: 42 + 35t = 49t
Simplify: 42 = 14t
Solve: t = 3

How many miles did car X travel from the time car Y began traveling until both cars stopped?
So, car X and car Y traveled for 3 hours (from the time car Y STARTED moving)
Car X's speed = 35 mph
So, car X's distance traveled (from the time car Y STARTED moving) = 3(35) = 105

Answer: A

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sat Mar 21, 2020 9:49 am

Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?

(A) 105
(B) 120
(C) 140
(D) 147
(E) 168

Answer: A
Source: Kaplan

Let t = the time car Y traveled before it stopped. Since 72 minutes = 72/60 hours = 6/5 hours, we can create the equation:

35(t + 6/5) = 49t

35t + 42 = 49t

42 = 14t

3 = t

So car X traveled 3 x 35 = 105 miles from the time car Y began travelling until both cars stopped.

Answer: A