Al is able to walk 25 miles in 25 minutes less time than Bob.Al and Bob walk at constant rates and Bob walks 1/4 mile per hour slower than Al. Find the speed at which Bob walks (in miles per hour).

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Let the speed of AL is `S_A`  and the speed of Bob is `S_B`

`` `==gt S_A = S_B +1/4`  mph...........(1)

Given a distance of 25 miles.

Let the time needed for AL to walk 25 miles is `T_A`  and the time for Bob is `T_B` .

`==gt T_A = T_B -25`  minutes

==> Now we will convert time to hours.

`==gt T_A = T_B - 5/12`  hours.............(2)

But we know that:

D = S*T = 25

Multiply (1) buy (2).

`==gt S_A*T_A = (S_B + 1/4 )(T_B - 5/12) `

`==gt 25 = (S_B)(T_B) + (1/4)T_B - (5/12)S_B - 5/48 `

`==gt 25 = 25 + (1/4)T_B - (5/12)S_B - 5/48 `

`==gt (5/12)S_B = (1/4)T_B - 5/48 `

`==gt S_B = (3/5)T_B - 1/4 But S_B = 25/T_B `

`==gt T_B = 25/S_B `

`==gt S_B = (3/5)(25/S_B) - 1/4 `

`==gt S_B = 5/(3S_B) - 1/4 `

`==gt 3(S_B)^2 = 5- 1/4 `

`==gt 3(S_B)^2 = 19/4 `

`==gt (S_B)^2 = 19/12 `

`==gt S_B~~ 1.26 mph`

Then the speed of Bob is 1.26 miles per hour. 

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