- a.The important concept in this problem is how rate, time, and distance interrelate. It is known that
distance = ratetime. We need to determine the amount of time that the girl is bicycling, and at pre-
cisely what time the girl and the instructor meet and have therefore traveled the exact same distance
from the starting point. So, we must determine expressions for the distances traveled by both the girl
and her instructor, then equate them. To this end, let x = number of hours the girl has been bicycling
when she intercepts her instructor. Then, since the instructor had a 3-hour head start, the amount of
time that he has been bicycling when the girl catches him must be 3 + xhours.
Now, write an equation for the girl, and one for the instructor that relates their respective times, rates,
and distance traveled.
Let Rg = rate of the girl = 17 mph
Tg = time the girl is bicycling when she meets her instructor = xhours
Dg = distance the girl has biked when she finally intercepts the instructor = 17x
RI = rate of the instructor = 7 mph
TI = time the instructor is bicycling when he meets the girl = 3 + xhours
DI = distance the instructor has biked when he is intercepted by the girl = 7(3 + x)
Using the information provided, we must solve the equation 17x = 7(3+ x), as follows:
17 x= 2(3 + x)
17 x= 21 + 7x
10 x= 21
x = 2.1
Thus, it takes the girl 2.1 hours (or 2 hours 6 minutes) to overtake her instructor.
- d.Let x= the amount invested at 10% interest. Then, she invested 1,500 + xdollars at 11% interest. The
amount of interest she earns in one year from the 10% investment is 0.10x, and the amount of interest
earned in one year from the 11% investment is 0.11(1,500 + x). Since her total yearly interest earned is
795 dollars, the following equation describes this scenario:
0.10x+ 0.11(1,500 + x) = 795
This equation is solved as follows:
0.10x+ 0.11(1,500 + x) = 795
0.10x+ 165 + 0.11x= 795
0.21x= 630
x= 06.^32 ^01 = 3,000
Hence, she invested $3,000 at 10% interest and $4,500 at 11% interest.
ANSWERS & EXPLANATIONS–
