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.
He does 4 runs and 6 walks.
1 minute 45 seconds = 1.75 minute
Let he does x runs and y walks.
So according to the question:
x+y=10
1.75x + 3y = 25
Solving them we get: x=4, y=6
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