Problem Solving

AAPL wrote:Magoosh

Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A's speed is 1.25 times Car B's speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A?

A. 60 mph
B. 75 mph
C. 80 mph
D. 96 mph
E. 100 mph

OA E.

Say the distance from the point Car A meets Car B to Town Y is x miles

Thus,

Car A traveled x miles in 105 minutes (= 3:15 pm - 1:30 pm) and Car B traveled (x - 35) miles in 105 minutes

Thus,

Speed of Car A = x/105 miles per minute = 60x/105 mph
Speed of Car B = (x - 35)/105 miles per minute = 60(x - 35)/105 mph

=> 60x/105 = 1.25 * 60(x - 35)/105; given that Car A's speed is 1.25 times Car B's speed

x = 175 miles

Speed of Car A = 60x/105 = (60*175)/105 = 100 mph

The correct answer: E

Hope this helps!

-Jay
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AAPL wrote:Magoosh

Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A's speed is 1.25 times Car B's speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A?

A. 60 mph
B. 75 mph
C. 80 mph
D. 96 mph
E. 100 mph

OA E.

From 1:30 pm to 3:15 pm, the time elapsed is 1 hour 45 minutes, or 1.75 hours. We see that during this time, Car A travels 35 miles more than Car B since its speed is 1.25 times that of Car B. Therefore, if we let r = speed of Car B, we can create the equation: .

(1.25r)(1.75) = 1.75r + 35

1.25(1.75r) = 1.75r + 35

1.25(1.75r) - 1.75r = 35

0.25(1.75r) = 35

1.75r = 140

r = 140/1.75 = 140/(7/4) = (4 x 140)/7 = 4 x 20 = 80

Since Car A's speed is 1.25 times the speed of Car B, Car A's speed is 1.25 x 80 = 100 mph.

Answer: E