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> [tex]5 \frac{1}{3}[/tex]
2. If distance traveled by Matthews is less than distance traveled by Carlos, then value of x is,
x < [tex]5 \frac{1}{3}[/tex]
3. If distance traveled by Matthews is equal to distance traveled by Carlos, then value of x is,
x= [tex]5 \frac{1}{3}[/tex]
So, we can't say who traveled greater distance between Matthew and Carlos.
