Math Algebra Question? Need Help Urgently!?

Question

Jake, Mel, and Annie went mountain biking on Mammoth Mountain. Each biker took a different trail. They biked for a total of 10 hours and 10 minutes. Mel biked 2/3 as long as Jake and Annie biked 30 minutes less than Jake did. How long did each of them bike?

This is the question. I know it can be solved with Guess and Check, but I need the algebraic way, and FAST!
Please don't tell me to solve it myself, because I have no idea for the technique. Please post the walkthrough and the once-over of the question on your answer.
Thank you SO much for answering this question! First decent answer posted with a clear description and why you did so and so, will be best answer.
May the best person win!
(I need the answer in a day, due Friday)

Answer 1

The total time the three of them biked is 10 hours 10 minutes, so:
J + M + A = 610 minutes
Mel biked for 2/3 as long as Jake, so:
M = 2J/3
The time Annie biked is 30 minutes less than Jake, so:
A = J - 30
Now that we know what A and M equal in relation to J, we can substitute them into the first equation:
J + 2J/3 + J - 30 = 610
And solve:
2J + 2J/3 = 640
6J/3 + 2J/3 = 640
8J/3 = 640
3(8J/3) = 3(640)
8J = 1920
8J/8 = 1920/8
J = 240, so Jake biked for 240 minutes.

Come back to the second equation, M = 2J/3, and we can solve for M:
M = 2J/3
M = 2(240)/3
M = 480/3
M = 160, so Mel biked for 160 minutes.

The third equation states that A = J - 30, which is solved:
A = J - 30
A = 240 - 30
A = 210, so Annie biked for 210 minutes.

Now we have all three variables.
J = 240
M = 160
A = 210
Jake biked for 240 minutes, or 4 hours.
Mel biked for 160 minutes, or 2 hours and 40 minutes.
Annie biked for 210 minutes, or 3 and a half hours.

Answer 2

Consider the information given and look for key words to clue you in on what to do. All three people biked for a total of 10 hours and 10 minutes. So if you add up each person's total time it will equal 10 hours and 10 minutes.
The times for each person are given in terms of what Jake did, so let Jake's time be x. Mel's time is 2/3x and Annie's time is 30 minutes less than Jake, or x-30. Since we're dealing with minutes, add all three together to equal 610 minutes, or 10 hours and 10 minutes.
x+2/3x+x-30=610. I added the two x's together to make it a little simpler.
Now you have 2x+2/3x-30=610

Get rid of the fraction by multiplying each term by three on both sides of the equal sign. 3(2x+2/3x-30)=3(610)This leaves you with
6x+2x-90=1830. Combine like terms.

8x-90=1830
Isolate the 8x by adding 90 to both sides of the equation:
8x=1920
divide both sides by 8
x=240

Jake's time was 240 minutes or 4 hours
Mel's time was 2/3 of Jakes or 160 minutes or 2 hrs 40 min
Annies time was 30 minutes less than Jake or 210 min or 3
hours and 30 minutes

Check by adding everything up 240+160+210=610
4 hours + 2hrs and 40 mins+3 hrs and 30 minutes=10 hrs 10 minutes.

Answer 3

Time = 610 minutes (10 hours X 60 minutes + 10 more minutes)

J + M + A = 610

Convert Mel and Annie into equations based on Jake:
M = 2J/3
A = J - 30

Substitute the Jake-based equations into the original equation:
J + 2J/3 + J - 30 = 610

Add 30 to both sides to get the variables on one side:
J + 2J/3 + J = 640

Simplify the J terms:
2J + 2J/3 = 640
...
8J/3 = 640

Multiply both sides by 3 to remove the fraction:
8J = 1920

Divide by 8:
J = 240

Jake rode 240 minutes. Now we can figure out the other two from our earlier equation:
M = 2J/3 = 160 minutes. Mel rode 160 minutes.
A = J - 30 = 210 minutes. Annie rode 210 minutes.

We check the result by adding them up:
240 + 160 + 210 = 610 minutes. It checks, so we're good.

Answer 4

So if you set the amount of time, in minutes, that jake bikes to x then the amount of time mel bikes is 2/3 times x, and the amount of time ann bikes is x - 30. The total time they bike is 10 hrs 10 min or 610 minute. So if you add all three algebric expressions together and set it equal to 610 minutes, (x-30)+(2x/3)+x = 610, you just need to solve for x. x turns out to be 240 minutes. There for Jake biked 240 minutes, mel biked 160 minutes, and ann bikes 210 minutes. Glad to help, email for any questions.

Answer 5

Let J be Jakes time.
M be Mel's time
A be Annie's time.
We know: J+M+A = 610 minutes (easier to do)
M= 2/3 J and A = J-30. We can substitute these two expressions in the total time eqtn to get
... 2-2/3 J = 640 and J= 240 min

Answer 6

Let Jason's age = J Let his older brother's age = B We know that J = 11 and that B = (2 x J) - 5 = (2 x 11) - 5 = 22 - 5 = 17 years old Now, for the younger brother: Let the younger brother's age = Y In 3 years, J will be J + 3 = 11 + 3 = 14 years old. We know that in 3 years, J, who will then be 14, will be twice as old as his younger brother so... In 3 years, Y + 3 = 14 / 2 Y + 3 = 7 So, now, Jason's younger brother is Y = 7 - 3 = 4 years old.