Question

Kim rode her bike at a rate of 24 km/h to the post office and 16 km/h back home. If her trip to the post office and back took a total of 75 minutes how far does Kim live from the post office?

Answer 1

Let's say x is the distance to the post office from Kim's home. Kim rides 2x km in 75 minutes. Half of the distance she rides at 24 km/h, and half she rides at 16 km/h. The time to ride the trip there is x (km) / 24 (km/h) = x/24 (h). The time to ride back is x (km) / 16 (km/h) = x/16 (h). We know that the two trips add up to 75 minutes. 75 minutes * 1 hour / 60 minutes = 5/4 hours.

\[\frac{x}{24} + \frac{x}{16} = \frac{5}{4}\]

Can you solve that for \(x\)?

Answer 2

not sure how to.

Answer 3

@NY,NY currently those fractional terms each have an uncommon denominator. Fractional terms can only be combined once they have like-denominators. What is your LCD, or Least Common Denominator?

Answer 4

2.

Answer 5

2 is a common multiple, but is not your least common denominator.

Answer 6

1?

Answer 7

Ok, forget trying to find a Least Common Denominator. What if we took the whole equation and multipled each term by 24? Try that.

Answer 8

You can also multiply the entire equation by 48, which is the least common multiple of those numbers. You can find the least common multiple by just writing like this:

4 8 12 16 20 24 28 32 36 40 44 48 52 56
16 32 48 64
24 48 72

48 is the first number that appears in each of the lists of multiples.

\[\frac{x}{24} + \frac{x}{16} = \frac{5}{4}\]Multiply by 48 gives
\[\frac{48x}{24} + \frac{48x}{16} = \frac{240}{4}\]And dividing those out
\[2x + 3x = 60\]
Now can you solve it?

Answer 9

24*((5/4)*hr*(1/2))*km/hr+16*((5/4)*hr*(1/2))*km/hr =25 km

Answer 10

@timo86m how about not just posting answers, especially wrong answers :-)

Answer 11

@whpalmer4
5x=60
x=12

Answer 12

RIght! So, we have an answer. Now is the important part: checking it!

If she rides 12 km at 24 km/h, it takes 1/2 hour (12/24). In the other direction, she rides 12 km at 16 km/h, so it takes (12/16) = 3/4 hour. 1/2 + 3/4 = 2/4 + 3/4 = 5/4. Our answer checks out.

Answer 13

Always, always, always check your answers for these problems...

Answer 14

right. thanks :)

Answer 15

And it's worth developing a sense of what a correct answer might be, too. timo86m said 25 km was the answer. Now, does that make sense? She rides her bike at only 24 km/h when she's going fast, so the fast trip would take a little more than an hour. There's no way she's going to get home in a quarter of an hour riding slowly, is there?

Answer 16

nope.