Question 970170: Alan & Sumei are 9km apart on a straight road and they are walking uniformly towards each other. If they start walking at the same time, they will meet in 1 hour 30 minutes. if Sumie starts walking 30 minutes after Alan, they will meet after Sumei has walked 1 hour 12 minutes. Find the speed of alan and the speed of sumei in km/h.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Alan & Sumei are 9km apart on a straight road and they are walking uniformly towards each other.
If they start walking at the same time, they will meet in 1 hour 30 minutes.
if Sumie starts walking 30 minutes after Alan, they will meet after Sumei has walked 1 hour 12 minutes.
Find the speed of Alan and the speed of Sumei in km/h.
:
let a = Alan's walking speed
let s = Sum's walking speed
:
When they meet they will have walked a total of 9 km
Write a dist equation for each scenario, dist = time * speed
:
1.5a + 1.5s = 9
simplify, divide equation by 1.5
a + s = 6
s = (6-a), use this form for substitution
and
Alan walks 30 min longer than Sum, 1 hr 42 min which is 1 + 42/60 = 1.7 hrs
Sum walks 1 hr 12 min which is 1 + 12/60 = 1.2 hrs
1.7a + 1.2s = 9
replace s with (6-a)
1.7a + 1.2(6-a) = 9
1.7a + 7.2 - 1.2a = 9
1.7a - 1.2a = 9 - 7.2
.5a = 1.8
a = 1.8/.5
a = 3.6 km/hr is Alan's walking speed
Find s
s = 6 - 3.6
s = 2.4 km/hr is Sum's
:
;
Check this in the 1st original equation
1.5(3.6) + 1.5(2.4) =
5.4 + 3.6 = 9
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