# How to work out average speed in problem solving question?

Jimmy and Dean were in a yacht race from Auckland to Suva, a distance of 1200km. Jimmy left port in Auckland two hours after Dean. He sailed at an average speed which was 2km/h faster than Dean and finished in Suva exactly one day before him

Given that the average speed is distance/time then find Dean's average speed during the yacht race.

I'm a bit confused ab out how to form the equation.

1200/x = 1200/(x+2) + 26

How come it becomes 26? I thought that the 2 hours head start was already covered by the 1200/x+2 ?

thanks.

• No. $x+2$ km/hr is the average speed of Jimmy, so the time required for Jimmy is $\dfrac{1200}{x+2}$ hrs. I think you got confused with $1200/(x+2)$ and $(1200/x)+2$. That's why it's always better practice to use parenthesis. Nov 20 '17 at 7:59
• Also to keep track of your units and understand what the variables actually mean. Since $x$ refers to the speed. The $2$ in $x+2$ definitely does not mean 2 hours. Nov 20 '17 at 8:20

If Dean's average speed is $x$, Jimmy's average speed is $x+2$.
The times it took them to travel are $\frac{1200}{2}$ and $\frac{1200}{x+2}$, respectively.
Now, since Jimmy started his trip $2$ hours later and arrives $24$ hours (1 full day) sooner, his travel time must, in total, be $26$ hours less than Dean's travel time. Thus we have
$$\frac{1200}{x} = \frac{1200}{x+2} + 26$$