Question

Jon recently drove to visit his parents who live 280 miles away. On his way there his average speed was 9 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 14 hours driving, find the two rates

Answer 1

Jon's two rates are 15 mph and 169 mph.

Step-by-step explanation:

To find Jon's two rates, let's assume his rate on the way to his parents' house is R mph. Then, his rate on the way back would be R-9 mph, as stated in the question. We can set up the equation:

Time to drive to parents' house + Time to drive back = Total driving time

280/R + 280/(R-9) = 14

Cross-multiplying and simplifying, we get:

R(R-9)=280(R-9)+280R

R^2-9R=280R-2520+280R

R^2-9R-560R+2520=0

R^2-569R+2520=0

Factoring the equation, we can find two values of R:

(R-15)(R-169)=0

R=15 or R=169

Since Jon's average speed cannot be negative, we can conclude that his rates are 15 mph and 169 mph.

Answer 2

11 mph and 20 mph

Step-by-step explanation:

Represent his average speed going by r1 and his average speed returning by r2. We know that r1 = r2 + 9.

Recall that distance = rate times time, so time = distance / rate.

Time spent going was (280 mi) / r1, or (280 mi) / (r2 + 9 mph).

Time spend returning was (280 mi) / r2.

The total time was 14 hrs, so (280 mi) / (r2 + 9 mph) + (280 mi) / r2 = 14 hrs

Note that there is only one variable here: r2. Find r2, and then from r2, find r1:

Dividing all 3 terms by 14 hrs yields:

20 20

---------- + ----------- = 1

r2 + 9 r2

The LCD here is r2(r2 + 9). Thus, we have:

20r2 (r2 + 9)(r2)

------------------- = 1 or ------------------

(r2 + 9)(r2) (r2 + 9)(r2)

Then 20(r2) = (r2)^2 + 9(r2). This is reducible by dividing all terms by r2:

20 = r2 + 9, or 11 = r2. Then r1 = 11 + 9, or 20.

The two rates were 11 mph and 20 mph.