It takes James five times longer
than it takes Olivia to get to work. If James’s journey is 70 minutes,
write an equation for the time 𝑥 it takes Olivia to get to work. Then solve the equation.
In this question, we need to write
an equation and then solve it. We’re told in the question that it
takes Olivia 𝑥-minutes to get to work. It takes James five times
longer. Five multiplied by 𝑥 is equal to
five 𝑥. Therefore, it takes James five 𝑥
minutes to get to work. We’re also told that James’s
journey time is actually 70 minutes. This means that we have a linear
equation five 𝑥 is equal to 70.
As we have now written the
equation, we can move on to the second part of the question, which is to solve
it. We know that James’s journey time
is 70 minutes. And we need to solve the equation
five 𝑥 equals 70 to work out Olivia’s journey time. This is a one-step equation as we
only need to carry out one calculation to solve it. Remember, we need to perform the
same calculation or operation to both sides of the equation. In this case, we will divide by
five. Dividing by five is the inverse or
reciprocal of multiplying by five.
Five 𝑥 divided by five is equal to
𝑥 as the fives cancel. 70 divided by five is equal to
14. If we couldn’t work out this
calculation mentally, we could use the short division bus stop method. Seven divided by five is equal to
one remainder two. And 20 divided by five is equal to
four. Therefore, 70 divided by five
equals 14. The solution of the equation five
𝑥 equals 70 is 𝑥 equals 14. We can therefore conclude that it
takes Olivia 14 minutes to get to work.
We can check this answer by
considering James’s time and multiplying five by 14. As 70 divided by five was 14, we
know that five multiplied by 14 must be equal to 70. Multiplication and division are the
opposite or reciprocal of one another. James’s journey time was 70
minutes, which is five times longer than Olivia’s of 14 minutes.