Math Help - 2 good old story problems

1. 2 good old story problems

Hey I am doing a graded homework and would like some help figuring out these story problems. I think I might have the right answer for the first one but I have no clue on the second one.

Mixture Problem: Billy likes to mix two cereals for breakfast. He wants to reduce his sugar intake without having to completely give-up Sugar-O's, his favorite cereal. Sugar-O's contain 20% sugar, while Health-Nut contains 5% sugar. How much of each cereal does he need in order to have a 25 g of a mixture that is 10% sugar?

Travel Time: You just got your license, so you are excited to drive on of the family cars on a driving family vacation. You are so excited that while your mom, who is driving the other car, travels at an average speed of 55 mph, you drive at an average speed of 68 mph. If you start out from home at the same time, and drive the same route, how much time will elapse before you are 15 miles ahead of your mom?

2. Originally Posted by exutable
I think I might have the right answer for the first one
That is great! Please show your methodology and someone will be delighted to confirm your answer or suggest any repairs that might be necessary.

On the second, you need only Distance = Rate * Time

MomDistance = Time * MomSpeed

KidDistance = Time * KidSpeed

We are given the speeds, leaving:

MomDistance = Time * 55 mph

KidDistance = Time * 88 mph

We are given a relationship for the distances.

KidDistance = MomDistance + 15 miles

This leaves

MomDistance = Time * 55 mph

MomDistance + 15 miles = Time * 88 mph

We're almost done. You're not going to make me do the WHOLE thing, are you?

3. Well for the second one I got 1 hour 9 minutes?

For the first one my original two equations were
x=sugar o's
y=Health-nut

x+y=25
.2x+.05y=25(.1)

I ended up getting y = 50/3 and x = 25/3

Is this right?

4. Originally Posted by exutable
For the first one my original two equations were
x=sugar o's
y=Health-nut

x+y=25
.2x+.05y=25(.1)

I ended up getting y = 50/3 and x = 25/3

Is this right?
that's correct. good job!

here's an alternate solution. it is very very similar to yours, but it gets rid of the simultaneous equations, so you can use it if you find those annoying

Let $x$ be the amount of Sugar O's in the mixture

then the amount of Health Nut in the mixture is $(25 - x)$

Thus we have: $0.2x + 0.05(25 - x) = 2.5$

solving that will give you the solutions you obtained

5. Oh and for the second one is the answer 1 hour 9 minutes?

6. Hello, exutable!

There is a back-door approach to the second problem.

While your mom travels at an average speed of 55 mph,
you drive at an average speed of 68 mph.
If you start out from home at the same time, and drive the same route,
how much time will elapse before you are 15 miles ahead of your mom?

You are driving: . $68 - 55 \:=\:13$ mph faster than Mom.

It is as if Mom is stopped and you are driving away at 13 mph.

How long will it take to drive 15 miles?

$\text{Time} \;=\;\frac{\text{Distance}}{\text{Speed}}$

. . $T \;=\;\frac{15\text{ miles}}{13\text{ mph}} \;=\;\frac{15}{13}\text{ hr} \:\approx\:1\text{ hr, }9\text{ min}$