1. ## Fractional Equations?

1) An intake pipe can fill a certain tank in 6 hours when the outlet pipe is closed, but with the outlet pipe open it takes 9 hours. How long would it take the outlet pipe to fill an empty tank?

2) Members of the ski club contributed equally to obtain $1800 for a holiday trip. When 6 members found that they could not go, their contributions were refunded and each remaining member then had to pay$10 more to raise the \$1800. How many went on the trip?

3) Because of traffic Maria could average only 40 km/h for the first 20% of her trip, but she averaged 75 km/h for the whole trip. What was her average speed for the last 80% of her trip?

4) A number x is the harmonic mean of a and b if 1/x is the average of 1/a and 1/b. Find two positive numbers that differ by 12 and have harmonic mean 5

2. Hello, Dunit0001!

Here's #3 . . .

3) Because of traffic Maria could average only 40 km/h for the first 20% of her trip.
But she averaged 75 km/h for the whole trip.
What was her average speed for the last 80% of her trip?

We know that: . $\text{Distance }\:=\:\text{Speed} \times \text{Time}$

. . and its variations: . $\text{Time} \:=\:\frac{\text{Distance}}{\text{Speed}}\qquad\te xt{Speed} \:=\:\frac{\text{Distance}}{\text{Time}}$

Suppose the trip was 400 km long.
The first 20% is 80 km; the last 80% is 320 km.

She drove 80 km at 40 kph.
. . This took her: . $\frac{80\text{ km}}{40\text{ kph}} \:=\:2$ hours.

The she drove 320 km at $x$ kph.
. . This took her: . $\frac{320}{x}$ hours.

Then, to drive 400 km, her total time was: . $2 + \frac{320}{x}$ hours.

Hence, her average speed was: . $\frac{400}{2 + \frac{320}{x}}$ kph.

Since her average speed was 75 kph, we have: . $\frac{400}{2 + \frac{320}{x}} \:=\:75$

. . Now solve for $x.$