Question

Word problems. ick.
Fan&Medal
Faith left town driving west at 50 mph. Gus left 3 hours later driving the same route at 65 mph. How many hours after Faith left will Gus to catch up to her? Round to the nearest tenth if necessary.
Select one:
a. 4.3 hours
b. 5 hours
c. 13 hours
d. 15 hours

Ted can paint a room in 10 hours and Vince can paint it in 11 hours. How long will it take the two working together? Round to the nearest tenth.
Select one:
a. 10.5 hours
b. 6 hours
c. 5 hours
d. 5.2 hours

Answer 1

Cashews cost $4 per pound and peanuts cost $1 per pound. How many pounds of peanuts should be used with the cashews to get a mixture of 24 pounds that will cost $2 per pound?
Select one:
a. 16
b. 9
c. 12.5
d. 6

Answer 2

Faith drives 50 mph, for 3 hours, before Gus starts driving. How far does she travel in that time?

Once Gus starts driving, he closes in on her by 65-50 = 15 mph. How long does it take to cover the distance of Faith's head start, going 15 mph?

Answer 3

Written as a formula, the distance Faith has gone in \(t\) hours is \(50t\). The distance Gus covers in \(t\) hours is \(65(t-3)\) because he doesn't drive for the first 3 hours.

The point where Gus catches Faith is when those two expressions are equal:
\[50t = 65(t-3)\]Distribute the expression on the right hand side and solve for \(t\). Note that @jjaed has demonstrated one of the hazards of accepting "help" from someone who doesn't show their work—you have no way of knowing if it is correct (hint: it isn't).

Answer 4

The painting problem is a rate problem. These are best worked by finding the rate of each worker individually, then combining the rates to find the time required. I'll do an example with different numbers:

Bob can paint a room in 4 hours
Steve can paint a room in 3 hours

Bob's rate is 1 room/4 hours = 1/4 room/hour
Steve's rate is 1 room/3 hours = 1/3 room/hour
Together, they do 1/4 + 1/3 room/hour, so it will take them
\[\frac{1}{\frac{1}{4} + \frac{1}{3}} = \frac{1}{\frac{3}{12} + \frac{4}{12}} = \frac{1}{\frac{7}{12}} = \frac{12}{7} = 1\frac{5}{7} \text{ hours}\]

Answer 5

@Issy14 no, because we divide by the rates, you can't take the average like that.

Answer 6

Mixture problem for the nuts:

cost of the cashew part of the mix is \(4c\) where the number of pounds of cashews is \(c\)
cost of the peanut part of the mix is \(1p\) where the number of pounds of peanuts is \(p\)

We have two equations:
\[c+p = 24\](the cashews + peanuts make 24 pounds)
\[4c+1p = 24*2\](the selling price of 24 pounds of the mix is $2/lb * 24 lbs, and we want the selling price to be the cost of the mixture)

You can solve that by substitution or elimination. If you don't know how to do that, I'm happy to explain (if you ask).

Answer 7

thanks so so much! @whpalmer4

Answer 8

You've got like 3 of the standard word problem types right here. If you get the underlying concept, you're good for dozens and dozens of problems :-)

There's a book called Word Problems Made Easy by Barbara Wingard-Nelson. You might see if your library has a copy, or whistle one up from a bookstore or Amazon.com. She covers pretty much every word problem type I've ever seen, clearly and has a nice collection of problems (with answers).