(1) My car gets 25 miles per gallon...

Problema Solution

(1) My car gets 25 miles per gallon for in-town driving, and 40mpg on the highway. if i

used 51 gallons on a recent trip of 1800 miles, how many miles were highway miles?

(2) Mixture A is 7.5% acid. To raise the concentration of acid to 10%, some pure acid will

be added to the mixture. how many Liters of mixture A and how many Liters of pure acid

are needed to end up with with 200 Liters of 10% solution?

(3) A bee leaves S at 3pm, and flies at 4mph on a straight line towards T. One half Hour

after the bee leaves S, a hornet leaves from S heading towards T along the same

straight line, flying at 5.5mph. At what time will the hornet catch the bee?

(1) Let 'x' represent the highway miles then '1800 - x' will represent the miles on in-town driving.

(1800 - x)/25 + x/40 = 51

........

........

x = 1,400 mi

1,400 miles were highway miles

(2) Let 'a' represent the liters of mixture A then '200 - a' represent the liters of the pure acid.

0.075a + 1.00(200 - a) = 0.10*200

........

........

a = 194.59 L

200 - 194.59 = 5.41 L

194.59 liters of mixture A and 5.41 liters of pure acid is needed for the 10% solution.

(3) Let 't' represent the time of the flight of the hornet then the time of the bee is 't + 0.5'.

Using the formula distance = speed*time we have:

4*(t + 0.5) = 5.5t

........

........

t = 4/3 hr

t = 4*60/3 min

t = 80 min

t = 1 hr 20 min

t + 0.5 = 1 hr 20 min + 30 min = 1 hr 50 min

1 hr 50 min after 3 pm is 4:50 pm.

The hornet will catch the bee at 4:50 pm.

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