SOLUTION: Tom and Jerry each walk 10 km. The speed of Tom is 1.5 times that of Jerry’s speed. Tom reaches the destination 1.5hrs before Jerry. Then Jerry’s speed is equal to (in km/hr)?

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Question 1191727: Tom and Jerry each walk 10 km. The speed of Tom is 1.5 times that of Jerry’s speed. Tom reaches the destination 1.5hrs before Jerry. Then Jerry’s speed is equal to (in km/hr)?
Found 3 solutions by Theo, greenestamps, josgarithmetic:
Answer by Theo(13342)   (Show Source):
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rate * time = distance formula for tom is 1.5 * r * (t - 1.5) = 10
rate * time = distance formula for jerry is r * t = 10
subtract the second equation from the first to get:
1.5 * r * (t - 1.5) - r * t = 0
simplify to get:
1.5 * r * t - 1.5^2 * r - r * t = 0
combine like terms to get:
.5 * r * t - 1.5^2 * r = 0
add 1.5^2 * r to both sides of the equation to get:
.5 * r * t = 1.5^2 * r
divide both sides of the equation by .5 * r to get:
t = 1.5^2 * r / (.5 * r)
simplify to get:
t = 1.5^2 / .5 = 4.5
substitute for t in r * t = 10 to get:
r * 4.5 = 10
solve for r to get:
r = 10/4.5

you have t = 4.5 and r = 10/4.5.
replace t with 4.5 and r with 10/4.5 in both original equations to get:
1.5 * r * (t - 1.5) = 10 becomes 1.5 * 10/4.5 * 3 = 10 which becomes 10 = 10.
r * t = 10 becomes 10/4.5 * 4.5 = 10 which becomes 10 = 10
this confirms the values of r and t are good.

your solution is that jerry's speed is equal to 10/4.5 kilometers per hour.
as a decimal that's equal to 2.22222...... kilometers per hour.
you may keep as a fraction or round the decimal equivalent as required.

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

Since Tom's speed is 1.5 = 3/2 times Jerry's, and the distances they walk are the same, the time Tom takes is 2/3 the time Jerry takes.

So let 2x and 3x be the numbers of hours it takes Tom and Jerry, respectively, to walk the 10km.

The difference in their times is then x; but we are told that difference is 1.5 hours.

So Tom's time for the 10km walk is 2x = 3 hours and Jerry's time is 3x = 4.5 hours.

And then Jerry's speed is 10/4.5 = 20/9 km/hr.

ANSWER: 20/9 km/hr

Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website!

SPEED TIME DISTANCE Tom 1.5j 10/(1.5j) 10 Jerry j 10/j 10 Difference 1.5

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