Question

On a three-day hike, Matthew hiked twice as much miles on the first day as on the second day. On the third day he hiked 5 miles. Carlos hikes 5 miles on the first day and three times as many miles on the second day as on the third day.

If Carlos hiked 4 miles on the third day, which boy hiked a greater total distance? Justify your answer using mathematics in the box below.

Answer 1

Distance hiked by Matthew

Matthew hiked twice as much miles on the first day as on the second day. On the third day he hiked 5 miles.

Distance traveled by Matthew on first day =2 x miles

Distance traveled by Matthew on second day = x miles

Distance traveled by Matthew on third day =5 miles

Total,Distance traveled by Matthew on total of three days =2 x+x+5=(3 x+5) miles

Distance hiked by Carlos

Carlos hikes 5 miles on the first day and three times as many miles on the second day as on the third day. Carlos hiked 4 miles on the third day.

Distance traveled by Carlos on first day= 5 miles

Distance traveled by Carlos on third day= 4 miles

Distance traveled by Carlos on Second day= 4 ×3=12 miles

Total Distance traveled by Carlos on total of three days= 5 +12+4=21 miles

As, Distance traveled by Matthews=(3 x+5) miles, on first and second day is a variable Quantity.So, we can't compare .

Three cases arises

1. If distance traveled by Matthews is greater than distance traveled by Carlos, then value of x is,

3 x +5 > 21

3 x >16

x>
`5 (1)/(3)`

2. If distance traveled by Matthews is less than distance traveled by Carlos, then value of x is,

x <
`5 (1)/(3)`

3. If distance traveled by Matthews is equal to distance traveled by Carlos, then value of x is,

x=
`5 (1)/(3)`

So, we can't say who traveled greater distance between Matthew and Carlos.