9514 1404 393
Answer:
- 5/2
- 8
- 65 mph, 62 mph
Step-by-step explanation:
The first two problems can be solved in your head by working backward from the end result.
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1. After 3/2 is added, the result is 4. Then we must be adding 3/2 to 4 -3/2 = 5/2. We notice that 5/2 already has the numerator 3 more than the denominator, so the fraction of interest is 5/2.
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2. If 3/8 is added to a number giving a result of 1, the number must be 1 -3/8 = 5/8. That is 5 times 1/8. The number of interest is the reciprocal of 1/8, so is 8.
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3. Let x represent the speed of the faster car. Then x-3 is the speed of the slower car, and the two times are ...
time = distance/speed
390/x = 372/(x-3)
390(x -3) = 372x . . . cross multiply
18x = 1170 . . . . . . . add 1170-372x
x = 65 . . . . . . . . . . divide by 18
The speeds of the cars are 65 mph and 62 mph.
