A man walks a certain distance with certain speed. If he walks 1/2km/h faster he takes 1 hour less. But if he walks 1km/h slower, he takes 3 more hours. Find the distance covered y the man and his otginal rate of walking.
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Answer:
If he walks 1/2 km/h faster ,he takes 1 hour less,but if he walks 1 km a hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking. Answer is Distance-36 and speed 4km/h
Step-by-step explanation:
MATHS
A man walks a certain distance with certain speed. If he walks
2
1
km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking
December 20, 2019avatar
Aaroohi Anju
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ANSWER
Let the original speed of the man=x km/hr
The schedule time of walking=y hrs.
∴ distance=yx km ..... Distance=Time×Speed
According to the first condition
increasedspeed=(x+
2
1
) km/hr
reducedtime=(y−1)hrs.
∴distance=(x+
2
1
)(y−1)
⇒xy+
2
y
−x−
2
1
In both case distance are equal
⇒xy=xy+
2
y
−x−
2
1
⇒y−2x−1⇔2x−y=−1 .......eq1
According to the second condition
reducedspeed=(x−1) km/hr
increasedtime=(y+3) hrs.
∴distance=(x−1)(y+3)
⇒xy−y+3x−3
In both case distance are equal
⇒xy=xy−y+3x−3⇒3x−y=3 ........eq2
Subtract eq 1 and eq2
⇒x=4
put x=4 in eq1
⇒2×4−y=−1
⇒−y=−9⇒y=9
Hence,The speed of the man=4 km/hr
The time of walking=9 hrs.
The distance covered by man 4×9=36 km.