SOLUTION: Hi this is a word problem that i need help with.
The school rowing team was practicing on the river. They were clocked by the coach and took 10 minutes to cover 1500 metres wit
Algebra.Com
Question 484763: Hi this is a word problem that i need help with.
The school rowing team was practicing on the river. They were clocked by the coach and took 10 minutes to cover 1500 metres with the current flowing against them. If there had been no current they would have taken 7.5 mintues.
How many kilometers an hour was the current flowing?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you can convert to kilometers and hours ahead of time, or you can solve in minutes and meters first and then convert to kilometers and hours.
we'll solve for minutes and meters first and then convert.
the basic formula used if rate * time = distance.
you are given time in minutes and distance in meters.
we set the rate of the boat as x.
we set the rate of the current as y.
going against the current, rate * time = distance becomes:
(x-y) * 10 = 1500
without any current, rate * time = distance becomes:
x * 7.5 = 1500
you have 2 equations that need to be solved simultaneously.
use the second equation to replace x in the first equation.
the second equation is 7.5*x = 1500
divide both sides of this equation by 7.5 to get x = 200
substitute for x in the first equation.
the first equation is (x-y) * 10 = 1500
substituting for x gets:
(200-y) * 10 = 1500
divide both sides of this equation by 10 to get:
200 - y = 150
subtract 200 from both sides of this equation to get:
-y = -50
multiply both sides of this equation by -1 to get:
y = 50
you have:
x = 200
y = 50
x is the speed of the boat
y is the speed of the current
the terms rate and speed are used inter-changeably. in this problem they mean the same thing.
substitute for and y in the original equations to see if these values are good.
7.5 * x = 1500 becomes 7.5 * 200 = 1500 becomes 1500 = 1500 which is true, confirming the value of x is good in the first equation.
(x-y) * 10 = 1500 becomes (200-50) * 10 = 1500 becomes 150 * 10 = 1500 becomes 1500 = 1500 which is true, confirming the value of x and y are both good in the second equation.
those are your answer.
they are, however in minutes and meters.
x = 200 means 200 meters per minute.
y = 50 means 50 meters per minute.
to translate meters to kilometers, you need to divide your meters by 1000.
your answer becomes:
x = .2 kilometers per minute
y = .05 kilometers per minute
to translate per minute to per hour, you need to multiply your minutes by 60.
your answer becomes:
x = 12 kilometers per hour.
y = 3 kilometers per hour.
12 kilometers per hour is the same as 12000 meters every 60 minutes.
divide it by 60 and you get 200 meters per minute.
3 kilometers per hour is the same as 3000 meters every 60 seconds.
divide it by 60 and you get 50 meters per minute.
the answers are equivalent.
you can also solve this problem by converting everything to kilometers and hours first and then solving.
if you did that, you would do the following.
1500 meters / 1000 = 1.5 kilometers
10 minutes / 60 = .167 hours
7.5 minutes / 60 = .125 hours
in your calculations use unrounded numbers rather than rounded numbers. store them in memory in your calculator and then recall them when you want to use them.
the two equations we have to work with were originally:
(x-y) * 10 = 1500
7.5 * x = 1500
those equations now becomes:
(x-y) * .167 = 1.5
.125 * x = 1.5
solve for x in the second equation to get:
x = 1.5 /.125 = 12 kilometers per hour.
use that value of x in the first equation to solve for y.
(x-y) * .167 = 1.5 becomes:
(12 - y) * .167 = 1.5
divide both sides of this equation by .167 to get:
12 - y = 9
subtract 12 from both sides of this equation to get:
-y = -3
multiply both sides of this equation by -1 to get:
y = 3
your answer are:
x = 12 kilometers per hour
y = 3 kilometers per hour
you got the same answer whether you used meters and minutes or you used kilometers and hours.
that confirms your answers are good.
the speed of the boat is 12 kilometers per hour.
the speed of the current is 3 kilometers per hour.
the time it takes without the current is 7.5 minutes which equals (7.5)/60 hours.
(7.5)/60 * 12 kilometers per hour = 1.5 kilometers which is equivalent to 1500 meters.
the time it take against the current is 10 minutes which equals (10/60) hours.
(10/60) * (12-3) = (10/60) * 9 = 90/60 = 1.5 kilometers which is equivalent to 1500.
everything checks out so you can be confident that the answer is good.
RELATED QUESTIONS
Hi I need help with this linear word problem please.
A total of 300 tickets were sold... (answered by rfer)
Please can you help me with the workings for this word problem as I am unable to do so:... (answered by ankor@dixie-net.com)
a basketball team scored 5 runs in a game which was four more than 1/2 the runs scored by (answered by greenestamps)
please explain this problem step by step. I am very confuse. seting up an equation in two (answered by ankor@dixie-net.com)
I need help with this problem:
Michael is practicing solving math problems every evening (answered by Theo)
I need help with this word problem please.
On three consecutive passes, a football team... (answered by Earlsdon)
I need help on this word problem I tried it and nothing worked out :/ --->
Two ships... (answered by Alan3354)
I need help setting up and answering this problem:
The speed of the current in a river... (answered by josgarithmetic,josmiceli)
I need help with a word problem please.
There are 980 students who attend high school. (answered by Earlsdon)