Wich number is the dividend and which is the divisor when it comes to finding unit prices

Question

How do I know which number to divide by when I have the following question: A runner completes a 10 km race in 0.75 hours. How long will it him take to complete 42 km? So I have to divide 10 and 0.75 and then I have to divide that answer and 42. What is the general rule for which number is the divisor and which is the dividend?

Answer 1

Often you can tell by looking at the units. The basic equation is distance(km)=speed (km/hr)*time (hr). You can see that the units agree in that they are km on both sides of the equation. Since speed is km/hr you divide the distance covered by the time to get $\frac {10}{0.75}$ km/hr speed. Now to get the time you divide the $42$ km distance by the speed in km/hr, giving a result in hr.

Answer 2

@Ross gave one way of looking at the problem, which was indicated to be required in your question. I shall suggest another (complementary) aporoach, with which you are undoubtedly familiar- The Unitary Method. A simple rule of thumb for such unitary method based problems -

Divide the quantity of the type you are required to find (here, time), with its corresponding quantity. Now, multiply it by the quantity for which you have to find the time.

That is -

• First, divide the given time (0.75 h) by its corresponding distance (10 km).

  • This gives the time taken to travel init (1 km) distance.

• Finally, multiply the obtained quantity by 42 km to find its corresponding time.

Required distance = $${(0.75 h) \over (10 \not km)} } \times (42 \not km) $$.

You can see how the distances cancel out to give time.

This approach is just as intuitive and useful as the other one.