SOLUTION: if a man travels at the speed of 40km/hr then he reaches the office 5min late and if he travels at the speed 50km/hr then he reaches 3min early,find the distance and time?

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Question 550222: if a man travels at the speed of 40km/hr then he reaches the office 5min late and if he travels at the speed 50km/hr then he reaches 3min early,find the distance and time?
Answer by ankor@dixie-net.com(22740) (Show Source):
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if a man travels at the speed of 40km/hr then he reaches the office 5 min late and if he travels at the speed 50km/hr then he reaches 3 min early, find the distance and time?
:
Let d = distance to the office
Let t - normal travel time to reach the office on time
:
change 5 min to hrs. 5/60 = 1/12 hrs
change 3 min to hrs: 3/60 = 1/20 hrs
:
write a time equation for each scenario
:
= t+; 5 min late
and
= t - : 3 min early
:
get rid of the denominators and rearrange both equations
= t+
Multiply by 120, results
3d = 120t + 10
3d - 120t = 10
and
= t -
multiply by 100, results
2d = 100t - 5
2d - 100t = -5
:
Multiply the 1st rearranged eq by 2, multiply the 2nd eq by 3:
6d - 240t = 20
6d - 300t = -15
----------------subtraction eliminates d, find t
+60t = 35
t =
t = 35 min is the normal time
:
Find d using the 5 min late equation (40 min travel time):(dist = speed * time}
*40 = 26.67 km is the distance
:
Confirm this using the 3 min early equation (32 min travel time)
* 50 = 26.67 km here also
:
Dist = 26.67 km, normal travel time 35 min