Answer:
It will take [tex]\frac{19}{101}[/tex] hour.
Step-by-step explanation:
The rule of the distance is:
Distance = speed × time
∵ An object is traveling at a steady speed of [tex]10\frac{1}{10}[/tex] km/h
∴ The speed = [tex]10\frac{1}{10}[/tex] km/h
∵ The object will travel [tex]1\frac{9}{10}[/tex] km
∴ The distance = [tex]1\frac{9}{10}[/tex] 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
∵ [tex]1\frac{9}{10}[/tex] = [tex]10\frac{1}{10}[/tex] × time
→ To find the time divide both sides by [tex]10\frac{1}{10}[/tex]
∴ The time = [tex]1\frac{9}{10}[/tex] ÷ [tex]10\frac{1}{10}[/tex]
→ Change the mixed numbers to an improper fraction
∵ [tex]1\frac{9}{10}[/tex] = [tex]\frac{(1)(10)+9}{10}=\frac{19}{10}[/tex]
∵ [tex]10\frac{1}{10}=\frac{(10)(10)+1}{10}=\frac{101}{10}[/tex]
∴ The time = [tex]\frac{19}{10}[/tex] ÷ [tex]\frac{101}{10}[/tex]
- Reverse the fraction after the division sign, then change ÷ to ×
∴ The time = [tex]\frac{19}{10}[/tex] × [tex]\frac{10}{101}[/tex]
→ 10 up will cancel 10 down
∴ The time = [tex]\frac{19}{101}[/tex] h
It will take [tex]\frac{19}{101}[/tex] hour.
