SOLUTION: Ramu travel to his home with speed of 5k/h he will reach 3 minutes late.if he go with speed of 6k/h he will reach 7minutes early.what is the distance he traveling?

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Question 979692: Ramu travel to his home with speed of 5k/h he will reach 3 minutes late.if he go with speed of 6k/h he will reach 7minutes early.what is the distance he traveling?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
t, target time
RT=D, basic uniform rate rule for travel
Ramu goes the same distance d, for both Is and If.

_________________rate___________time____________distance
IS_______________5______________t+3/60___________d
IF_______________6______________t-7/60___________d

5%28t%2B1%2F20%29=6%28t-7%2F60%29

5t%2B1%2F4=6t-6%287%2F60%29

5t%2B1%2F4=6t-7%2F10

20%2A5t%2B20%2F4=20%2A6t-20%287%2F10%29

20%285t-6t%29%2B20%2F4=-14

-20t%2B5=-14

20t-5=14

20t=19

highlight_green%28highlight%28t=19%2F20%29%29-------THIS IS STILL CORRECT------same as 57 minutes------Use this time to find d.

FINDING DISTANCE d:

At 5 k/h,
5%2857%2F60%2B3%2F60%29=5%2860%2F60%29
highlight%28d=5%29

At 6 k/h,
6%2857%2F60-7%2F60%29
6%2850%2F60%29
%286%2F60%29%2A50
%281%2F10%29%2A50
highlight%28d=5%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Ramu travel to his home with speed of 5k/h he will reach 3 minutes late.if he go with speed of 6k/h he will reach 7minutes early.what is the distance he traveling?
Let distance be D

At 5 km/h, it took him a time of D%2F5 to get home

At 6 km/h, it took him a time of D%2F6 to get home

Since a time of D%2F5 makes him 3 minutes late, then "on-time" time = D%2F5+-+3%2F60, or D%2F5+-+1%2F20

Since a time of D%2F6 makes him 7 minutes early, then "on-time" time = D%2F6+%2B+7%2F60

Setting "on-time" times equal, we get: D%2F5+-+1%2F20+=+D%2F6+%2B+7%2F60

12D - 3 = 10D + 7 ----------- Multiplying by LCD, 60

12D - 10D = 7 + 3

2D = 10

D, or distance = 10%2F2, or highlight_green%285%29 km