speed time and distance math word problem

Question

Up Town and Down Town are 420 km apart. Mr. A left Up Town for Down Town at an average speed of 75 km/h. At the same time, Mr. Z left Down Town for Up Town at an average speed of 93 km/h along the same road. How far would Mr. A travel when he passed Mr Z. along the way?

Answer 1

Let t be the time at which they pass each other.

 

Mr. A will have traveled 75t km and Mr. Z 93t km.

 

75t + 93t = 420 (since between the two of them, they covered the entire length of road.

 

Solving for t: 168t = 420 -> t = 2.5 hours

 

Mr. A traveled 75 * 2.5 or 187.5 km

Answer 2

Hi Julius;

 

If Mr. A drives x km

Mr. Z drives (420-x)km

 

Using distance formula  d = rt and noting they drive for the same

amount of time up to the point they meet:

 

Mr. A:  x = 75t

Mr. Z:  420-x = 93t

 

A:  t = x/75

Z:  t = (420-x)/93

 

x/75 = (420-x)/93

cross multiply

93x = 75(420-x)

93x = 75(42) - 75x

168x = 31500

x = 187.5 km

 

Mr. A travels 187.5 km to the meeting point

Mr. Z travels 420-187.5 = 232.2 km the meeting point

 

Note this makes sense because Mr. A was driving slower and thus didn't go as far.