Question

It takes Max 1 minute and 45 seconds to run around a track once. It takes Max 3 minutes to walk one lap on the same track. If Max walks and runs around the track and completes 10 laps in 25 minutes, how many laps did he run?

Answer 1

Answer:

4 laps running

Step-by-step explanation:

Les r be the number of laps he completed running an w the number of laps he walked. Also, lets write all in seconds, which can be a little easier than working with minutes.

Then, as it takes him 1:45 minutes by running, and we know that 1 minute is equal to 60 seconds, we can say it takes him 60+45=105 seconds to run a lap.  Then, as it takes him 3 minutes to walk a lap we can say it takes him 3*60=180 seconds to walk a lap.

Thus, in total the minutes he needs if he runs r laps and walk w laps is:

time = 105 r + 180 w

As we know he did his laps in 25 minutes, which are equivalent to 25*60=1500 seconds:

105 r + 180 w = 1500 [equation 1]

We also know he completes 10 laps, which means that"

r + w = 10 [equation 2]

We can subtract w (or r) in both sides of equation 2 to get the value of r as a function of w:

r = 10 - w [equation 2']

Then we can plug equation 2' in equation 1 leaving all in terms of w:

105 r + 180 w = 1500

105 (10 - w) + 180 w = 1500

1050 - 105 w + 180 w = 1500

1050 + 75 w = 1500

If we subtract 1050 in both sides:

75 w = 1500 - 1050

75 w = 450

Dividing both sides by 75 we get the value of w:

w = 450/75

w = 6

So, he walked 6 laps. Then, he must have run the remaining 4 laps.