linear equation word problems

Question

Two cyclists start at the same point and travel in opposite directions. One cyclist travels
4/kmh faster than the other. If the two cyclists are 248km apart after 4 hours, what is the rate of each cyclist?

Answer 1

If the two cyclists start at the same point, and travel in opposite directions, they are moving away from each other in a straight line.

 

First, lets see the total distance traveled by both cyclists is equal to 248 km. If you divide this number by 4, you get 62. This is allowed because the rate is not changing, otherwise the problem would tell you. Dividing by 4 lets us know the distance that has formed between the two cyclists in 1 hour. 

 

Now, one cyclist is 4 kmh faster. You can write an equation relating the two: x + (x+4) = 62

 

Then, solve for x: 2x+4 = 62, 2x = 58, x =29

 

So, the rate of one cyclist is 29 kph, and the other cyclist is going at 33 kph.

 

One way you can check this answer, is to multiply both answers by 4, then adding them. Remember that each cyclist rode for 4 hours. 

 

4hours*29kmh= 116km, 4 hours*33kmh= 132km, 132km+116km= 248km.

 

Note I am stressing the units because it can (and will) affect the answer your put down. Just be mindful that some teachers might want you to convert your answer to meters or centimeters, so be ready to alter your final answer as necessary in order to answer the question completely.