Question

Jill was going to meet at the bus depot if she went during rush hour she would travel 15 mph and arrive 1 hour later if she went after rush hour she would travel 30 mph and arrive an hour early

Answer 1

The distance cover by Jill is 60 miles

Explanation:

Given as :

The speed of Jill to cover the distance D during rush hour = 15 mph

Let The usual time taken to cover D distance = T hour

So, The time taken to travel during rush hour = ( T + 1 ) hour

The speed of Jill to cover the distance D after rush hour = 30 mph

And The time taken to travel after rush hour = ( T - 1 ) hour

Now,According to question

Distance = Speed × Time

Now, For during rush hour

D = 15 × ( T + 1 )

Or, D = 15 T + 15 ........A

Again , For after rush hour

D = 30 × ( T - 1 )

Or, D = 30 T - 30 ..........B

Solving Eq A and B

I.e 15 T + 15 = 30 T - 30

Or, 15 + 30 = 30 T - 15 T

or, 45 = 15 T

∴ T =
`(45)/(15)`

I.e T = 3 hour

So, The usual Time taken = T = 3 hour

Put the value of T in eq A

I.e D = 15 T + 15

Or, D = 15 × 3 + 15

∴ D = 60 miles

So, Distance = D = 60 miles

Hence The distance cover by Jill is 60 miles . Answer