Question

An object is traveling at a steady speed of 10 1/10 km/h. How long will it take the object to travel 1 9/10 km?

Answer 1

It will take
`(19)/(101)` hour.

Explanation:

The rule of the distance is:

Distance = speed × time

∵ An object is traveling at a steady speed of
`10(1)/(10)` km/h

∴ The speed =
`10(1)/(10)` km/h

∵ The object will travel
`1(9)/(10)` km

∴ The distance =
`1(9)/(10)` km

→ We need to find how long will it take it to travel this distance

→ Substitute the values of distance and speed in the rule above

∵
`1(9)/(10)` =
`10(1)/(10)` × time

→ To find the time divide both sides by
`10(1)/(10)`

∴ The time =
`1(9)/(10)` ÷
`10(1)/(10)`

→ Change the mixed numbers to an improper fraction

∵
`1(9)/(10)` =
`((1)(10)+9)/(10)=(19)/(10)`

∵
`10(1)/(10)=((10)(10)+1)/(10)=(101)/(10)`

∴ The time =
`(19)/(10)` ÷
`(101)/(10)`

- Reverse the fraction after the division sign, then change ÷ to ×

∴ The time =
`(19)/(10)` ×
`(10)/(101)`

→ 10 up will cancel 10 down

∴ The time =
`(19)/(101)` h

It will take
`(19)/(101)` hour.