Question

The clarke family went sailing on a lake their boat averaged 6 kilometers per hour the rourke family took their outboard runabout for a trip on the lake for the same amount of time their boat averaged 14 kilometers per hour the rourke family travled 20 kilometers farther than the clarke family how many hours did each family spend on their boat trip?

write an algebraic equation and salve it

Answer 1

We'll use the distance-rate-time formula: d = rt. Only first, we'll change it's form so that we're looking at time instead of distance. So, t = d/r.

We do this because the time both families were out is the same so by setting their individual d/r values equal to each other, we elliminate a variable.


Let the distance the Clarke family traveled by C. So their boating time was C/6
The Rourke family traveled 20km more than the Clarke family, so their boating time is (C+20)/14

Set these equal to each other...\[\frac{C}{6}=\frac{C+20}{14}\]

Solve for C...then back substitute this value into C/6 to find the time spent on the boating trip...

Answer 2

ok how do i salve

Answer 3

Cross multiply. 14 * C = 6 * (C + 20). Distribute the 6, gather all variable on one side and constants on the other...

Answer 4

i dont know algera have not taken it in 8 years

Answer 5

Ok...I'll walk you through this one as a refresher :) But then you're on your own... :)

Answer 6

i have lots of these for homework

Answer 7

After the cross multiplication, you have
14C = 6(C + 20)
14C = 6C + 120 <-- Distributed the 6 into the parentheses
14C - 6C = 6C - 6C + 120 <-- Moving the C terms to one side of the equals
8C = 120
C = 15 <-- Divided both sides by 8 to get C alone

So this says that the Clarke family traveled 15km during their boating trip. Sin ce they traveled at 6km/hr, 15/6 = 3.5 is the length of time they spent boating.

So they (and the Rourke family since they were said to be equal) boat spent 3.5 hours boating.

Make sense?

Answer 8

a little i didnt have this kinda stuff when i took it 8 years ago

Answer 9

Did you at least understand the steps after the cross multiplication? If so, you're a good step forward. Everything else is set-up which is problem dependent. For anything involving distance, rate, and time, the formula I used is the key...then you look for what is the same for both groups involved.

Set up your forumla so that that piece is on one side and everything else is on the other side and fill in the variables based on what they gave you.

Answer 10

they only give me questions and dont show me how to write them and work them out i looked in my book but i didnt see how to make a equation

Answer 11

You have another one we can work through? After another one, it might start to click...

Answer 12

i have seven more

Answer 13

Let's just try one...the idea being that at some point you'll understand them enough to not need my help :)

Answer 14

five-sixths of a number is -60 what is the number

Answer 15

you there

Answer 16

Sorry...had to step away for a second

Answer 17

Anytime you don't know the value of something, assign it a variable. So we want to find a particular number. Let's call it x.

five-sixths of the number is 5/6 times the number (Key math fact: the word "of" translates into math as "times")

So we have\[\frac{5}{6}x=-60\]

Answer 18

The number in front of the variable is called the coefficient. In this case, the coefficient is 5/6

Since the x term is by itself on the left, to solve, all we need to do is divide both sides by the coefficient.

Dividing by a fraction is the same as multiplying by its reciprocal.

Answer 19

So,\[\frac{5}{6}x = -60\]\[\frac{6}{5}\times\frac{5}{6}x=-60\times\frac{6}{5}\]\[x=\frac{-60}{1}\times\frac{6}{5}=-12(6)=-72\]

Answer 20

Did you follw that?

Answer 21

that is over my head sorry

Answer 22

Which part is over your head? Tell me where I lose you and I can try to explain it differently.

Answer 23

if your cross muiltp how are you getting-12*6=-72

Answer 24

so is the answer x=-72

Answer 25

Ahh...ok...In this case I didn't *need* to use cross multiplication since i don't have a variable on both sides. I *can* use cross multiplication though.

\[\frac{5x}{6}=\frac{-60}{1}\]\[1\times5x=-60\times 6\]\[5x=-360\]\[x=-72\]

Answer 26

ok so 5x * 1 = 5x and 6*-60 =-360 *5 on both sides and the two fives cancel out and i am going to get x=-72

Answer 27

Yes...once you have 5x = -360, you divide both sides by 5...the fives on the left cancel and -360/5 = -72.

Starting to make some sense?

Answer 28

yeah some sorry my baby cryed can we do another one

Answer 29

Unfortunately, I'm leaving work now. If you post your questions, there are a lot of good people on now. They can certainly help you. Just remember, if you don't understand a step they did, ask why they did it. They are more than happy to give additional explanation as long as you're specific about where you got lost.

The worst thing to say on here is a general, "I'm confused" in response to an answer. Math takes a while to get back into once you've been out for a while...I don't think you'll need too much more help before it starts to come back.

Good luck and if I see more questions from you later, I'll do my best to help.

Answer 30

ok