manson get up every day at 8:am to go to the work if he drives at an average speed of 60 miles per hour he will be late by 6 minutes if he drives at an average speed of 90 miles per hour he will be early by 6 minutes how many miles per hour does manson need to drive to get to work exactly on time
Answers
Answer:
Step-by-step explanation:
Answer:
If he drives at an average speed of 72 miles / hr. he will reach the work exactly on time.
Step-by-step explanation:
Let x miles be the distance between the home and his work place.
And t hr. is the time taken by him to reach at the work exactly on time.
We know that distance will remain same in both the cases .
When he drives at an average speed of 60 miles /hr.
Distance = Speed × Time
x = 60 × { t+ (6 / 60)} ,,,,,,,,,,,,, (1)
When he drives at an average speed of 90 miles / hr.
x = 90 × { t - ( t - ( 6 /60)} ,,,,,,,, (2)
As distance is same ,so from eq (1 ) and (2)
60 {t + (6 /60 )} = 90 { t -( 6/60)}
Dividing both side by 30 we get,
2 { t + (1/10 ) } = 3 { t - (1/10)}
2t + (2/10) = 3t - ( 3/10)
(2/10 ) + (3/ 10) = 3t - 2t
(2 +3 )/10 = t
5/ 10 =t
1/2 = t
Putting the value of t in eq. (1)
x= 60 { ( 1/2) + (6/60 )}
= 60 { (1/2) + (1/10)}
= 60 {(5+1) /10} = 60 { 6/10) =36 miles
Required speed = distance /time
= 36 /(1/2) = 36× 2= 72 miles / hr.