"Mixture" and "Distance, Speed, and Time" Word Problems

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October 3rd 2011, 05:55 PM
aspiringphysician

"Mixture" and "Distance, Speed, and Time" Word Problems

Hello,

I have three algebra word problems that I have literally spent hours working on, and I feel extremely stupid because I cannot figure out how to set them up to get the correct answer! (Headbang) Any help would be greatly appreciated! (Nod)

Here goes:

1. A radiator in a car - with a capacity of 3.7 liters - is filled with a solution of 60% antifreeze and 40% water. How much coolant should be drained and replaced with water to reduce the antifreeze concentration to 50%?

2. A pilot flew a jet from Montreal to Los Angeles, a distance of 2500 miles. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 9 hours and 10 minutes. What was the speed from Montreal to Los Angeles?

3. A salesman drives from Ajax to Barrington, a distance of 120 miles, at a steady speed. He then increases his speed by 10 mph to drive the 150 miles from Barrington to Collins. If the second leg of his trip took 6 minutes more than the first leg, how fast was he driving between Ajax and Barrington?

Thanks in advance!
October 3rd 2011, 06:19 PM
TKHunny

Re: "Mixture" and "Distance, Speed, and Time" Word Problems

Find something that you can track.

Radiator

1: 3.7 litre * 0.60 = Amount of Coolant at the start.
2: We'll be draining x litre, and that's x litre * 0.60 of coolant.
3: We'll be adding x litre of water. That's x litre * 0 = 0 litre coolant.
4: W need to end up with 3.7 litre * 0.50 total coolant

Then 3.7*0.6 - x*0.6 + x*0.0 = 3.7*0.50

If you would prefer to equate the water, you may. It is very nearly the same

Then 3.7*0.4 - x*0.4 + x*1.0 = 3.7*0.50

Sometimes one or the other is a little easier. The one with the zero (0) usually wins that contest.

Solve both and convince yourself.
October 3rd 2011, 08:32 PM
Soroban

Re: "Mixture" and "Distance, Speed, and Time" Word Problems

Hello, aspiringphysician!

Quote:

2. A pilot flew a jet from Montreal to Los Angeles, a distance of 2500 miles.
On the return trip, the average speed was 20% faster than the outbound speed.
The round-trip took 9 hours and 10 minutes.
What was the speed from Montreal to Los Angeles?

Let $x$ = outbound speed.
Then $1.2x$ = return speed.

He flew 2500 miles outbound at $x$ mph.
. . This took $\tfrac{2500}{x}$ hours.

He flew 2500 mile back at $1.2x$ mph.
. . This took $\tfrac{2500}{1.2x}$ hours.

$\text{The total time was: }\:\text{9 hours, 10 minutes} \,=\,9\tfrac{1}{6}\text{ hours} \,=\,\tfrac{55}{6}$ hours.

There is our equation . . . . $\dfrac{2500}{x} + \dfrac{2500}{1.2x} \;=\;\dfrac{55}{6}$

. . . Go for it!
October 17th 2011, 02:50 PM
aspiringphysician

Re: "Mixture" and "Distance, Speed, and Time" Word Problems

Sorry...I've been busy lately...thanks so much for your help!!!!!