Question

Will medal or fan please help!!!
A train travels 42 kilometers in 15 minutes. How far will the train travel in 3 hours at that speed?

A.
168 km

B.
336 km

C.
504 km

D.
672 km

Answer 1

@whpalmer4

Answer 2

1 hour = 60 minutes
3 hours = 3x60 = 180 minutes

15 minutes ----> 42 km
180 minutes ----> x

x = 180*42/15

Answer 3

Figure out the rate. 42 kilometers/ 15 minutes = how many kilometers per minute?

Answer 4

\(\large{ 3hrs\implies 60mins\cdot 3\implies 180mins
\\ \quad \\

\begin{array}{ccllll}
km&mins\\
\hline\\
42&15\\
x&180
\end{array}\implies \cfrac{42}{x}=\cfrac{15}{180}}\)

Answer 5

itwould be 2.8 kilometers a minute but where do I go from their? I think you would do what @hoblos did... with the x= 180*42/15 right?

Answer 6

is it possible I could do something like... so I would cross multiply to find the value of x

Answer 7

distance traveled is given by \[d = r t\]where \(r\) is the rate or speed, and \(t\) is the time. You'll multiply the rate by the time to get the distance. Notice that you need to convert to consistent units, because the time is in hours, and the rate is in km/minute

\[d = rt\]\[d = \frac{42 \text{ kilometers}}{15 \text{ minutes}} * \frac{60 \text{ minutes}}{1 \text{ hour}} * 3 \text{ hours}\]\[ = \frac{42 \text{ kilometers}}{15 \cancel{\text{ minutes}}} * \frac{60 \cancel{\text{ minutes}}}{1 \cancel{\text{ hour}}} * 3 \cancel{\text{ hours}} \]\[=\frac{42*60*3}{15} \text{ kilometers}\]\[=\text{________ kilometers}\]

Answer 8

Good to learn how to do proper unit conversions, which build in a check against error. If the units don't cancel into the units you want, you've done the conversion incorrectly.

Answer 9

or set up the problem incorrectly

Answer 10

is it possible to cross multiply because if so I have my answer... 504?

Answer 11

it is possible to do this as a proportion, yes, but you still need to do the unit conversion somewhere. This is a simple problem, where you may not be likely to mess up the conversion, but if you learn how to do the conversion correctly on simple problems, it will be a tried and true procedure when you have more complicated problems where messing up the conversion is more likely.

Answer 12

Say the initial speed is 42 km in 15 minutes, but I want the distance traveled in 2.5 days, expressed in furlongs? You can do that as a proportion, too :-)

Answer 13

In any case, 504 km is the correct answer.

Answer 14

oh okay thank you @whpalmer4 I got the right answer then... yay!!!

Answer 15

Set up a ratio! :D

Answer 16

Thanks! :D