On Monday, you run on a treadmill for #1/2# hour at #x# miles per hour. On Tuesday, you walk the same distance on the treadmill, at #2# miles per hour slower, and it takes you #3/4# hour. How many miles did you run on the treadmill on Monday?

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Answer 1 · 2017-05-29T16:46:49

#3# miles run on Monday

It is useful to summarise the information in the form of a table with columns for distance, speed and time.

Remember if you know two of these, you can write an expression or answer for the third one.

#s= d/t and t = d/s and d = sxxt#

We have that the speed on Monday was #x# miles per hour and the time, #1/2# an hour. We can find the distance as #x xx 1/2#

Show this on the table and then complete it for Tuesday as well.

#color(white)(wwwwww)ul("Distance Speed Time")#

Monday#|" "1/2xcolor(white)(wwwww)xcolor(white)(wwwww) 1/2#

Tuesday#|" "1/2xcolor(white)(wwww)(x-2)color(white)(www) 3/4#

The speed on Tuesday can be given in two ways:

It is the same as on Monday #(1/2x)" "# or as #" "s xx t#

Form an equation: #3/4(x-2) = 1/2x#

#4xx3/4(x-2) =4xx 1/2x" "larrxx 4#

#3(x-2) = 2x#

#3x-6 = 2x#

#x = 6" "larr# this was the speed on Monday.

The distance run on Monday was #1/2 xx6 = 3# miles