(WORD PROBLEM) Solving Systems

Question

A bicyclist heads east at 19 km/h. After she has traveled 22.5 kilometers, another cyclist sets out in the same direction going 28 km/h. About how long will it take the second cyclist to catch up to the first cyclist?

 

Thank you in advance!

Answer 1

The first cyclist traveled 22.5 km at 19 kph so he traveled 22.5/19 = 1.18421 hr

We can convert this to minutes: 60+1.18421 = 71.05 minutes or just 71 minutes

 

If the first cyclists time is X,the second cyclist leaves at X - 71 minutes

 

Now we set the two cyclists time equal to each other, multiplied by their respective speeds in minutes.

 

60*19 kphX = 60*28 kph(X-71)

1,140X = 1,680(x-71)

1,140X = 1,680X - 119,280

 

Solve for X

 

-540X = -119,280

X = -119,280 / -540 = 220.89 or about 221 minutes

 

It will take 221 minutes or 3 hrs and 41 minutes to catch up with the first cyclist.