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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