Answer: Time taken by him in going = 8 hours
Time taken by him in returning = 9 hours
Step-by-step explanation:
Let the total distance from home to New York is x miles,
[tex]\text{ Since, Time} = \frac{\text{Distance}}{\text{Speed}}[/tex]
Also, he drove his car from his home to New York at the rate of 45 mph,
⇒ [tex]\text{ Time taken by him in going } = \frac{x}{45}\text{ hours}[/tex]
And, returned over the same road at the rate of 40 mph.
⇒ [tex]\text{ Time taken by him in returning } = \frac{x}{40}\text{ hours}[/tex]
According to the question,
Time taken by him in returning - Time taken by him in going = 30 minutes = 1/2 hours, ( 1 hours = 60 minutes )
⇒ [tex]\frac{x}{40}-\frac{x}{45}=\frac{1}{2}[/tex]
⇒ [tex]\frac{9x}{360}-\frac{8x}{360}=\frac{1}{2}[/tex]
⇒ [tex]\frac{x}{360} = \farc{1}{2}[/tex]
⇒ [tex]2x=720[/tex]
⇒ [tex]x=360\text{ miles}[/tex]
Hence, the total distance from home to New York = x miles = 360 miles
⇒ [tex]\text{ Time taken by him in going } = \frac{x}{45}\text{ hours}[/tex]
[tex]=\frac{360}{45}=8\text{ hours}[/tex]
⇒ [tex]\text{ Time taken by him in returning } = \frac{x}{40}\text{ hours}[/tex]
[tex]=\frac{360}{40}=9\text{ hours}[/tex]
Answer:
It took him 4 hours to get there and 4.5 hours to get back.
Step-by-step explanation:
