algebra and rate

[tRNA]

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Got 2 more math problems for u....

1) when 2 is added to the numerator of the fraction y/x, the fraction equals 1/4. When 2 is added to the denominator of y/x, the fraction equals 1/5. What is y/x? answer: 10/48

I know how to solve it the long way by substitution but it takes ~4min and is error prone, what's shortest way to do it??

2) a river flows at 3mph. A man can row at 5mph in still water. If he rows 1 mile upstream and then floats back to the starting place, how many minutes will be required for the roundtrip? answer: 50

I set up this chart, let me know if correct and how to proceed , thanks

d= r x t
upstream-->d= 1 r= 5+3 t=x
downstream-->f d=1 r= 3 t=x
total d=2

 

[StephL26]

2) a river flows at 3mph. A man can row at 5mph in still water. If he rows 1 mile upstream and then floats back to the starting place, how many minutes will be required for the roundtrip? answer: 50

I set up this chart, let me know if correct and how to proceed , thanks

d= r x t
upstream-->d= 1 r= 5+3 t=x
downstream-->f d=1 r= 3 t=x
total d=2

Use common sense in this one...

I just assumed that river was flowing downstream (saves time when calculating), and since the man has to row OPPOSITE, 5-3mph is 2mph. So he's rowing 1 mile upstream at 2 mph. 5mi/1hr = 1 mi/ (X) hr, so X= 1/2 hr, which is 30 min. Then going with the FLOW at 3mph, we have 3mi/1hr = 1 mi / X, and X is now 1/3 of an hour, that's 20 min. So 30+20 minutes = 50 minutes.

I didn't use your setup above since I don't quite follow what you're doing there 😀 , I find that when I do it my way, I get answer under 1 minute. Good luck.

 

[Streetwolf]

Got 2 more math problems for u....

1) when 2 is added to the numerator of the fraction y/x, the fraction equals 1/4. When 2 is added to the denominator of y/x, the fraction equals 1/5. What is y/x? answer: 10/48

I know how to solve it the long way by substitution but it takes ~4min and is error prone, what's shortest way to do it??

(y+2)/x = 1/4
y/(x+2) = 1/5

x = 4(y+2) (first equation)
y/(4y+10) = 1/5 (plug into second equation)
5y = 4y + 10
y = 10
x = 48

Not so tough. Probably the best way.

2) a river flows at 3mph. A man can row at 5mph in still water. If he rows 1 mile upstream and then floats back to the starting place, how many minutes will be required for the roundtrip? answer: 50

I set up this chart, let me know if correct and how to proceed , thanks

d= r x t
upstream-->d= 1 r= 5+3 t=x
downstream-->f d=1 r= 3 t=x
total d=2

No. Upstream is against the current. So he travels at 5-3 = 2mph in 1 hour. Thus he needs 30 minutes. Then on the trip back the river takes him at 3mph. He needs to go 1 mile so it takes 20 minutes. Total is 50 minutes.