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A Word Problem That Makes You A Mathematician by Tahtah: 7:17am On Nov 19, 2016
A cyclist cycles for x hours at 12km/hour and y hours at 18km/hour. Altogether she cycles 78km in 5hours. Find x and y
Re: A Word Problem That Makes You A Mathematician by Nobody: 8:52am On Nov 19, 2016
Don't know, but let me give it a try: grin
.
By definition:
Speed = Distance / Time
.
For x hours:
78km / 5+x = 12km/hr
.
78 = 12(5+x)
78 = 60 + 12x
12x = 78 - 60
12x = 18
x = 3/2hrs
.
.
For y hours:
78km / 5+y = 18km/hr
.
78 = 18(5+y)
78 = 90 + 18y
18y = 78 - 90
18y = -12
y = -2/3hrs
.
Please if I'm wrong, then criticize me constructively and NOT destructively. Happy solving!
Re: A Word Problem That Makes You A Mathematician by Dermie: 9:25pm On Nov 19, 2016
Tahtah:
A cyclist cycles for x hours at 12km/hour and y hours at 18km/hour. Altogether she cycles 78km in 5hours. Find x and y

From shortcut/guess work... 12*2=24, 18*3=54; 2+3=5hrs, 24+54=78km... Therefore x=2hrs, y=3hrs.

From long solution:

12x + 18y = 78km (eqn 1)
x + y = 5 hrs (eqn 2)

Multiply (eqn 2) by 12

12x + 18y = 78 (eqn 3)
12x + 12y = 60 (eqn 4)

Subtract (eqn 4) from (eqn 3) to solve for y

6y = 18
y = 18/6
y = 3

Solve for x using (eqn 2)

x + 3 = 5
x = 5 - 3
x = 2

Therefore x=2hrs, y=3hrs.

2 Likes

Re: A Word Problem That Makes You A Mathematician by Tahtah: 9:53pm On Nov 19, 2016
Dermie:


From shortcut/guess work... 12*2=24, 18*3=54; 2+3=5hrs, 24+54=78km... Therefore x=2hrs, y=3hrs.

From long solution:

12x + 18y = 78km (eqn 1)
x + y = 5 hrs (eqn 2)

Multiply (eqn 2) by 12

12x + 18y = 78 (eqn 3)
12x + 12y = 60 (eqn 4)

Subtract (eqn 4) from (eqn 3) to solve for y

6y = 18
y = 18/6
y = 3

Solve for x using (eqn 2)

x + 3 = 5
x = 5 - 3
x = 2

Therefore x=2hrs, y=3hrs.
Nice solution

1 Like

Re: A Word Problem That Makes You A Mathematician by Dermie: 10:03pm On Nov 19, 2016
Tahtah:

Nice solution

Any award available? cheesy
Re: A Word Problem That Makes You A Mathematician by Nobody: 10:21pm On Nov 19, 2016
Nice one bro!

1 Like

Re: A Word Problem That Makes You A Mathematician by Dermie: 2:44am On Nov 21, 2016
Laive:
Nice one bro!

Thanks bro
Re: A Word Problem That Makes You A Mathematician by Tahtah: 11:08am On Nov 24, 2016
Dermie:


Any award available? cheesy
Yes, pls wink
Re: A Word Problem That Makes You A Mathematician by Dermie: 1:19pm On Nov 26, 2016
Tahtah:

Yes, pls wink

Alright. Let me know when it's ready smiley

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