How do u solve this math ?

Question

Grace leaves ome at 8:00 am. Ten minutes later, will notices grace's lunch and begins bicycling after her. If grace walks at 5 km/h and will cycles at 15 km/h, how long will it take him to catch up w/ her?

Answer 1

Equate distances and solve for time.

graces distance: 5*10 + 5*t
will's distance: 15*t

Note that I've started the clock when will starts. That's because the question asks how long will must ride.

Now, just equate the distances and solve for t.

I get 5 minutes.

grace = 50+25 = 75
will = 5*15 = 75

Btw, I graphed these on my TI-83 and looked for the intersection. It's helpful to draw the lines.

Answer 2

These word problems can be fun (because once you know how to set them up, they're also EASY). But so many students start out 'afraid' of word problems... at least this type of exercise is truly useful later in life!

In this case, you must visualize the two people moving in the same direction. Ignore the fact that they make the trip at different times; just concentrate on the fact that they "catch up" with one another ... so (this is important) they travel the SAME DISTANCE!

That is: distance(Grace) = distance(Will)

The most useful formula for this problem is "the distance formula": Rate * Time = Distance

Rate is the speed of a traveler, and we know both rates: rate(Grace) = 5, rate (Will) = 15

We may not immediately know the actual distances both people travel, but the fact that they are equal is very helpful. How?

Distance1 = Distance2

We substitute now:

Rate1 * Time1 = Rate2 * Time2

Now, write in all the given information. The only way we can represent Time1 and Time2 is by T and (T-10) -- because Will's travel time is 10 minutes less (he started at 8:10).

So:

5 * T = 15 * (T-10)

Multiply:

5T = 15T - 150

Collect like terms:

-10T = -150

Divide:

T = 15 minutes

Grace walked for 15 minutes before Will caught up, which means the clock read 8:15 am.

How long did Will ride, then? Only 5 minutes.

Hope this helps!

Answer 3

1 hr. = 60 min.
set up a porportion: a = the distance grace covers in 10 min
(5km/60min) = (a/10min)
a = .8333333 km
set up a system of equations for grace and will:
grace: y = 5x + .83
will: y = 15x
since grace starts 10 min before will leaves the house, you have to take into account the distance she covers before he leaves the house. Grace's slope is 5 because she is travelling at 5km an hour. Will's slope is 15 because he is travelling at 15 km an hour.
set the two equations equal to each other:
5x + .83 = 15x
x = .08333333
multiply x by 15 because to find the distance it takes for will to catch up with grace
15x = 1.25 km
set up a porportion: b = the time it takes for will to catch up with grace (use will's slope to find b)
(1.25km/b) = (15km/60min)
b = 5 min

Answer:
5 min.

Answer 4

We know that Will travels three times faster than Grace. The amount of time Will travels will be the variable "x" and the amount of time Grace travels will be three times Will's time or 3x. Will's time plus the 10 minutes Grace has already traveled will equal Grace's total time.

x+10=3x

subtratct one "x" from each side

10=2x

divide each side by 2

5=x

In five minutes (1/12th of an hour), Will travels 1/12th of 15k or 15/12 which simplifies to 1.25k. In 15 minutes (1/4th of an hour), Grace travels 1/4th of 5k or 5/4 which also simplifies to 1.25k

Answer 5

use the equation

time=distance/speed

first find the distance that grace has covered which is
0.167*5=0.835

so wiil needs 2 cover a distance of 0.835 2 catch up2 grace so....

0.835/15=0.056

convert that back in2 mins...

aprox...3.34mins
its approx coz theres a slight error margine due 2 rounding off

or without doing all that u could just say that will is going 3 times as fast as grace...therfore his time would b.....

15/5=3

Answer 6

suppose t is time in minutes he catch up her (=t/60 h.)
grace bycycled for (t+10) miute=(t+10)/60 h
distance=velocity*time
the distance of grace d=(t+10)*5/60 km
the distance of will d=t*15/60 km
both reach to the same place(distance) from home
(t+10)*5/60=t*15/60
5t+50=15t
10t=50
t=5 minutes

Answer 7

It will be 3 minutes because you would have to divide 15 by 5 to get the answer.

Answer 8

may be he wont be able to get ot Grace as she might have already reached the school (if school is not too far), but if school is far there are chances for will to catch Grace.

Answer 9

its 3, you divide how fast grace is going by how fast will is going-(15 divided by 5)

Answer 10

How? With a calculator, very carefully

A real hint: remember that concept Mr. Physics teacher taught called RELATIVE VELOCITY...Try it out.