This is the solution for the time and distance algebra word problem #9 that read:

"if I walked 9 laps around a track. One lap is 1312 ft. I walked at a rate of 4 miles an hour. how many minutes did it take me to walk 9 laps?"

The easiest way to think about this problem is to think about an easier problem and then copy the steps. What if the problem read:

if I walked 9 laps around a track -- 1 lap is 1 mile and i walked at a rate of 4.5 miles and hour. how many minutes did take me to walk 9 laps?

well the total distance would be the length of 1 lap: 1 mile * the # of laps which is 9 --> 9 * 1 = 9 miles

the rate was 4.5 miles an hour -- distance = rate * time

so 9 miles = 4.5miles/hour* time

9 miles/4.5 miles/hour = time or 2 hours would be how long it would take--->

So this is not a hard math problem the arithmetic is what's hard in this problem, but if you just follow the same steps you will get the answer easily enough. So, again we have:

"if I walked 9 laps around a track. One lap is 1312 ft. I walked at a rate of 4 miles an hour. how many minutes did it take me to walk 9 laps"

ok so take 9 * 1312 1st to get the total distance in feet which is : 11808

4 miles an hour would be (5280 ft in a mile) 5280 * 4 = 21120 ft/hour

But we dont want hours we want minutes-- there are 60 minutes in an hour

so (21120 ft*1hour)/(hour*60minutes) --> you're multiplying by 1hour/60 minutes. so divide by 60..

362ft/minute --- the hours(1 hour = hour) cancel out..

*** **Correction** -- user Donaldson pointed out I made a division error -- I said 362 feet should be 352 feet/min...*** Thanks!

ok so now we have a total distance in feet of 11808 feet -- divided by the rate of 352 ft/minute

11808 ft/(352 ft/minute) = 11808 ft *minute/ 352 ft

the ft cancel out you divide 11808 by 352 and get 33.54545 = 33.55 minutes --> which is a good enough answer but if you want it more exact:

.545454 of 60 seconds would be 60 *.5454 = 32.72 seconds == approx 33 seconds --- so 32 minutes 33 seconds would be a more recognizable (as far as common usage of time) answer.

You can kind of double check the answer by making sure its reasonable when you see that the total distance of 11808 feet that you walked is roughly 2 miles and your dividing by 4 miles an hour=== 1/2 an hour or 30 minutes approximately

## Tuesday, August 25, 2009

### Time and Distance Problem 9 Solution

## Sunday, August 2, 2009

### Plane Geometric Figure Problem 1 Solution

This is the solution to the Plane Geometric Figure Problem 1 which asked you to "find the dimension of a rectangle whose length is 9 less than twice its width if the perimeter is 120 cm."

In a rectangle 2 times the width plus to times the length equals the total perimeter.

Let the width equal x

Then the length is equal to 2x - 9 which means "9 less than twice its width"

Remember 2 times the width plus to times the length equals the perimeter so..

2(x) + 2(2x - 9) = 120

which is..

2x + 4x - 18 = 120

6x - 18 = 120

6x = 120 + 18

6x = 138

x = 138/6

x = 23

Since we let x stand for the width then the width of the rectangle is 23 cm and the length is 2(23) - 9 = 46 - 9 = 37

So the width is 23 cm and the length is 37 cm

Check 2(23) + 2(37) = 120

46 + 74 = 120

120 = 120

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### Age Problem 4 Solution

This is the solution to the algebra age problem # 4... "A man is 27 years older than his son and 10 years from now, he will be twice as old as his son. how old is each now?"

Let x = the son and x + 27 = the man(father)

in 10 years the son will be x + 10 and the father x + 27 + 10 or x + 37 years old. So if he will be twice as old as his son then "twice" the sons age then will "equal" each other.

So, 2(x+10) = x + 37

multiply by 2 on the left side

2x + 20 = x + 37

x = 17 This makes sense since 10 + 17 = 27 and 17 + 37 = 54 which is twice the sons age 10 years from now. So the son is 17 and the father is 17 + 27 or 44 years old.