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# If Leah is 6 years older than her sister, Sue, and John is 5

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Manager
Joined: 27 Sep 2006
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If Leah is 6 years older than her sister, Sue, and John is 5 [#permalink]  20 Nov 2006, 18:05
1. If Leah is 6 years older than her sister, Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?

2. Two cyclists start biking from a trailâ€™s start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

what are the solutions?
could you recommend a website that lays out problems for each kind?

thanks!
Director
Joined: 18 Jul 2006
Posts: 531
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Kudos [?]: 28 [0], given: 0

Sue's Age = x
Leah's Age = x+6
John's Age = (x+6) + 5
x+(x+6)+(x+6+5) = 41
3x+17=41
This gives x=(41-17)/3=8
---------
Suppose A and B are cyclists.
A starts first (@6 miles/hr) and bikes for 3 hrs. Distance travelled = 6x3 = 18 miles
Distance between A and B = 18 miles.
Difference between A's and B's speed = 10-6 = 4 m/h
Time taken = 18/4 = 4 1/2 hrs.
Senior Manager
Joined: 01 Sep 2006
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Location: Phoenix, AZ, USA
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1. If Leah is 6 years older than her sister, Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?

(1)L = S + 6
(2) J = L + 5
L+J= S+L+11
Cancel out L
J = S+11
We know
L+S+J = 41
Substitute L=S+6 and J = S+11
S+6 + S + S+11=41
3S=41-11-6=24
S=8

2. Two cyclists start biking from a trailâ€™s start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

In 3 hour 1st cyclist has lead of 6*3=18 miles

2nd has to overcome this lead to catch up

Diff of speed b/w 1st and nd cyclist = 10 miles - 6 miles = 4 miles

5nd cyclist gains 4 miles in 1 hour
so he gains 18 miles in 18/4=4.5 hours
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