The running speed of the man is <u>16 km/hr.</u> and his walking speed is <u>6 km/hr.</u>, solved using the system of equations.
In the question, we are given that a man travels 10km in 50mins if he runs for 8km and walks for 2km. If he runs 4km and walks 6km, his time is 1h 15mins.
We are asked to find his running and walking speed.
We assume the running speed to be r km/hr., and the walking speed to be w km/hr.
<u>In the first case:-</u>
Distance he ran = 8km.
Thus, the time for which he ran = 8/r hr.
Distance he walked = 2km.
Thus, the time for which he walked = 2/w hr.
Thus, the total time = 8/r + 2/w.
But, we are given that in the first case, he took 50 mins = 5/6 hours.
Thus, we get an equation, 8/r + 2/w = 5/6, or, 4/r + 1/w = 5/12 ... (i).
<u>In the second case:-</u>
Distance he ran = 4km.
Thus, the time for which he ran = 4/r hr.
Distance he walked = 6km.
Thus, the time for which he walked = 6/w hr.
Thus, the total time = 4/r + 6/w.
But, we are given that in the first case, he took 1 h 15 mins = 5/4 hours.
Thus, we get an equation, 4/r + 6/w = 5/4 ... (ii).
(i) and (ii) together gives us a system of equations.
Subtracting (i) from (ii), we get:
4/r + 6/w = 5/4.
4/r + 1/w = 5/12.
(-) (-) (-)
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5/w = 10/12 = 5/6.
or, w = 6.
Substituting w = 6 in (ii), we get:
4/r + 6/w = 5/4,
or, 4/r + 6/6 = 5/4,
or, 4/r = 1/4,
or, r = 16.
Thus, the running speed of the man is <u>16 km/hr.</u> and his walking speed is <u>6 km/hr.</u>, solved using the system of equations.
Learn more about the system of equations at
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The provided question is incomplete. The complete question is as follows:
"A man travels 10km in 50mins if he runs for 8km and walks for 2km. If he runs 4km and walks 6km, his time is 1h 15mins. find his running and walking speed."
