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Question

2 planes travel toward each other from cities that are 2975km apart at rates of 440km/hr and 410km/hr. They started at the same time. In how many hours will they meet?

Answer 1

Hi Trey.

 

If you set up a diagram (it is hard to make a pretty diagram here, but here goes...) showing the total distance between the two cities, and the point where the planes meet, it can be reprsented like:

 

|<----D1--------->|<------------------D2-------------------------->|

0                       meet                                                   2975km

 

D1 is the distance plane 1 travels = (440 km/hr)*(time in hours) = 440t

D2 is the distance plane 2 travels = (410 km/hr)*(time in hours) = 410t

 

And we know that D1+D2 = 2975

Substituting for the D1 and the D2, we get 440t + 410t = 2975

 

Simplify the left side:  850t = 2975

 

Divide both sides by 850 to isolate "t"

 

t = 3.5 hours

 

 

NOW CHECK:  In 3.5 hours Plane 1 travels 1540 km   (found by 440 * 3.5)

                        In 3.5 hours Plane 2 travels  1435 km  (found by 410 * 3.5)

                        Add these to see that 1540 + 1435 = 2975  and we know that we have the right answer.

 

|<---- 1540 km --------->|<----------------- 1435 km -------------------------->|
0                                meet                                                                 2975km

 

 

|<----D1--------->|<------------------D2-------------------------->|

0                       meet                                                   2975km