Two cars start at the same point and travel in opposite directions. If

Question

Two cars start at the same point and travel in opposite directions. If one car travels at 45 miles per hour and the other at 60 miles per hour, how much time will pass before they are 210 miles apart?

(A) 0.5 hours 
(B) 1 hour 
(C) 1.5 hours 
(D) 2 hours 
(E) 2.5 hours

Leo8 · Accepted Answer

Two cars start at the same point and travel in opposite directions. If one car travels at 45 miles per hour and the other at 60 miles per hour, how much time will pass before they are 210 miles apart?

There are two ways to solve this one:
{1} Find the relative speed between two cars and find the time taken: \(\frac{210}{ relative speed : 45+60}\) = \(\frac{210}{105}\) = 2 hours

{2} Find the relationship between the two car's speed.
for every 60 miles car 1 travels, car 2 travels 45 miles
that is : for every 4 mile car1 travels, car2 travels 3 miles

So car 1 and car 2 will cover the distance 210 miles in part : 4:3

let x be the factor for the distance travelled by car 1 and car2 : 4x + 3x = 210 ; x = 30

so car 1 drove = 4 * 30 = 120 miles
car 2 drove = 3 * 30 = 90 miles

time taken by car 1 to travel = time taken by car 2 to travel = \(\frac{120}{60}\) = \(\frac{90}{45}\) = 2 hours

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Luckisnoexcuse · Answer

relative speed is 105 miles per hour and they will take 2 hrs to be 210 miles apart

Option D

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generis · Answer

When cars travel in opposite directions, whether away from or toward one another, add their respective rates.

45 + 60 = 105 mph

rate * time = distance --->

D/r = t

Distance is 210 miles.

210 miles / 105 mph = 2 hours

generis · Answer

Though frequently used and technically accurate, just want to note that "relative speed" can be confusing in the context of cars moving in opposite directions (whether coming toward each other or moving away from one another). In the latter scenario, "relative" also means "combined speeds where rates are added." (IMO "relative" makes more intuitive sense when you think of the "chase," where cars are moving in the same direction and slower rate is subtracted from faster rate.) Done. Now please pay it forward. ;-)

Leo8 · Answer

genxer123 By relative speed, I meant effective speed. I would say both Car 1 and Car 2 were spreading apart with a rate of 105 miles per hour. This speed is not the exact speed of car 1 or car 2 but the effective speed at which they are moving apart. I don't see any confusion in calling this as relative speed. you could have a chase scenario , a crash scenario - in both the cases , it is recommended to calculate the relative speed / effective speed of the whole action. and Thanks for the Kudos

Skywalker18 · Answer

Relative speed of both cars = 45+60 = 105 miles per hour
Distance = 210 miles
Time = 210/105 = 2 hours

Answer D

ScottTargetTestPrep · Answer

Since we have a diverging rate problem, we can use the following formula:

distance of car 1 + distance of car 2 = 210

We can let t = the time traveled by either car, and thus the distance of car 1 is 45t and the distance of car 2 is 60t. Thus:

45t + 60t = 210

105t = 210

t = 2 hours

Answer: D

kartikesh8375 · Answer

Two cars start at the same point and travel in opposite directions. If one car travels at 45 miles per hour and the other at 60 miles per hour, how much time will pass before they are 210 miles apart?

(A) 0.5 hours
(B) 1 hour
(C) 1.5 hours
(D) 2 hours
(E) 2.5 hours

t = distance btw them / speed a + speed b
so
210 / 105 = 2 
formula is based on relative speed as they are going in opp direction so both speed need to be added

bumpbot · Answer

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