SOLUTION: Kim and tom both cyclic to work from their homes, at the same speed. kim lives 20km away from work, and tom lives only 15km away from work. it takes kim 1 hour more to cycle to wor

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Question 1184529: Kim and tom both cyclic to work from their homes, at the same speed. kim lives 20km away from work, and tom lives only 15km away from work. it takes kim 1 hour more to cycle to work than tom. determine how long tom takes to get to work
Found 4 solutions by ikleyn, Theo, greenestamps, MathTherapy:
Answer by ikleyn(52848)   (Show Source):
You can put this solution on YOUR website!
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Kim and tom both cyclic to work from their homes, at the same speed. kim lives 20km away from work, and tom lives only 15km away from work.
it takes kim 1 hour more to cycle to work than tom. determine how long tom takes to get to work
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Let r be their rate, in kilometers per hour, the same for both. Kim's time is hours; Tom's time is hours. The difference of times is 1 hour, which gives you this "time" equation - = 1 hour. To solve it, multiply both sides by r. You will get 20 - 15 = r or r = 5. So, their rate is 5 km/h, the same for both. Tom's travel time is 15/5 = 3 hours. ANSWER

Solved.

Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
R * T = D

for tom, the formula becomes R * T = 15

for kim, the formula R * (T + 1) = 20

solve for R in both equations to get:

for tom, R = 15 / T

for kim, R = 20 / (T + 1)

since both equations are equal to R, then you get:

15 / T = 20 / (T + 1)

multiply both sides of the equation by T * (T + 1) to get:

15 * (T + 1) = 20 * T

simplify to get:

15 * T + 15 = 20 * T

subtract 15 * T from both sides of the equation to get:

15 = 20 * T - 15 * T

simplify to get:

15 = 5 * T

solve for T to get:

T = 3 hours.

T + 1 is therefore 4 hours.

for tom, R * 3 = 15.
solve for R to get:
R = 15/3 = 5 km per hour.

because the rate for each is the same, the two formulas now become:

for tom:

5 * 3 = 15 which becomes 15 = 15, which is true.

for kim:

5 * 4 = 20 which becomes 20 = 20, which is true.

the formulas are both true when R = 5 km per hour and T for tom is 3 and T for kim is 4.

your solution is that it takes tom 3 hours to get to work.

Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!

You have received two responses that show very different valid algebraic solutions to the problem. You should understand both solutions, since they show good algebraic methods.

But this problem can also be solved VERY quickly without formal algebra, using logical reasoning.

The speeds are the same for both, so the ratio of times is the same as the ratio of distances.

The ratio of distances is 20:15 = 4:3, so the ratio of times is 4:3.

If the ratio of times is 4:3 and Kim takes 1 hour longer than Tom, then Kim takes 4 hours to ride to work and Tom takes 3 hours.

ANSWER: It takes Tom 3 hours to get to work

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

Kim and tom both cyclic to work from their homes, at the same speed. kim lives 20km away from work, and tom lives only 15km away from work. it takes kim 1 hour more to cycle to work than tom. determine how long tom takes to get to work

Let time it takes Tom to cycle to work, be T Then time it takes Kim to cycle to work is: T + 1 Since they travel at the same speed, we then get the following SPEED equation: 4T = 3T + 3 ------ Cross-multiplying 4T - 3T = 3 Time it takes Tom to cycle to work, or