Bob is training for a race. Bob ran 14.6 miles away from his home. Then, Bob ran 9.8 miles towards his home Finally, Bob ran 5.3 miles away from his home. How far is Bob from his home?

1 Answer
Johnson Z.
Apr 5, 2016

#10.1# miles

Explanation:

Bob's training can be broken down into three steps:

#1#. ran #14.6# miles away from home

#2#. ran #9.8# miles towards his home

#3#. ran #5.3# miles away from his home

Since Bob starts running from his home, he is #0# miles from his home.

If he starts running from his home for #14.6# miles, you would add #14.6# miles to #0# miles to indicate how far Bob ran for his first run. For this problem, when Bob travels away from home, you add the distance he travels. In contrast, when he travels towards his home, you subtract the distance he travels.

#0color(white)(i)"miles"+14.6color(white)(i)"miles"#

When Bob runs towards his home at a distance of #14.6# miles away from his home, you subtract #9.8# miles from #14.6# miles since he is now going in the opposite direction in which he was originally heading.

#0color(white)(i)"miles"+14.6color(white)(i)"miles"-9.8color(white)(i)"miles"#

Finally, when Bob runs #5.3# miles away from his home, opposite to the direction of his second run, you must add #5.3# miles.

#0color(white)(i)"miles"+14.6color(white)(i)"miles"-9.8color(white)(i)"miles"+5.3color(white)(i)"miles"#

If you solve the addition problem, you get #10.1# miles.

#:.#, Bob is #10.1# miles from his home.

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