1hour/60minutes vs 60minutes/1hour

[xbyxeqwhat]

There's this problem I ran into on khan academy.

"
Starting at home, Omar traveled uphill to the gift store for 303030 minutes at just 101010 mph. He then traveled back home along the same path downhill at a speed of 3030 mph.
What is his average speed for the entire trip from home to the gift store and back?
"
I'm confused about how they carry out the calculation. distance uphill=speed uphill×time uphill
=10 mph × 30 minutes × 1 hour/60 minutes
=5 miles


time downhill=distance downhill/speed downhill=
=5 miles/30 mph × 60 minutes/1 hour
=10 minutes

What I'm confused about is how do you know in which case to put hour over minutes or minutes over hours.

 

[Deleted member 4993]

There's this problem I ran into on khan academy.

"
Starting at home, Omar traveled uphill to the gift store for 303030 minutes at just 101010 mph. He then traveled back home along the same path downhill at a speed of 3030 mph.
What is his average speed for the entire trip from home to the gift store and back?
"
I'm confused about how they carry out the calculation. distance uphill=speed uphill×time uphill
=10 mph × 30 minutes × 1 hour/60 minutes
=5 miles


time downhill=distance downhill/speed downhill=
=5 miles/30 mph × 60 minutes/1 hour
=10 minutes

What I'm confused about is how do you know in which case to put hour over minutes or minutes over hours.

You know that

mph →\(\displaystyle \dfrac{mile}{hour}\)

So for the first problem you converted 30 minutes to 1/2 hour (dividing 30 by 60). You HAVE to do this otherwise your dimensions will not come to "miles"(dimension of distance)

For the second, your answer is 1/6 hour - then you converted that to minutes (by multiplying the result with 60).

 

[xbyxeqwhat]

@10mph.....5m...........>1/2h (uphill)
1/6h<........5m............@30mph (downhill)

May I nervously ask: why d'heck do we "see" the likes of 303030?

Oh, I'm sorry. For some reason it copied that way, I thought I fixed it. It's supposed to be just 30 minutes, 10mph and 30mph.