Question

A student runs 3 1/3 miles in 30 minutes. A teacher runs 1 1/4 times as far in 30 minutes. How far can the teacher run in 30 minutes?

Answer 1

The distance cover by teacher in 30 minutes is 4
`(1)/(6)` miles .

Explanation:

Given as :

The distance cover by student = d = 3
`(1)/(3)` miles

i.e d =
`(10)/(3)` miles

The time taken by student to cover
`(10)/(3)` miles distance = t = 30 minutes

Let The speed of student = s miles per minute

∵ Speed =
`(\textrm Disatnce)/(\textrm Time)`

Or, s =
`(d)/(t)`

Or, s =
`((10)/(3))/(30)`

i.e s = 0.111 miles per min

So, The speed of student = s = 0.111 miles per min

Now, Again

The speed of teacher = 1
`(1)/(4)` times as fast as student

Let The speed of teacher = S miles per min

∵ The speed of teacher =
`(5)/(4)` × speed of student

So, S =
`(5)/(4)` × s

Or, S =
`(5)/(4)` × 0.111 miles per min

Or, S =
`(5* 0.111)/(4)` mil/min

i.e, S = 0.13875 miles per min

So, The speed of teacher = S = 0.13875 miles per min

Let The distance cover by teacher = D miles

The time taken by teacher to cover D miles distance = T = 30 minutes

∵ Distance = Speed × Time

Or, D = S × T

Or, D = 0.13875 miles per min × 30 min

∴ D = 4.1625 miles

i.e D = 4
`(1)/(6)` miles

So, The distance cover by teacher in 30 minutes = D = 4
`(1)/(6)` miles

Hence,The distance cover by teacher in 30 minutes is 4
`(1)/(6)` miles . Answer