Explanation :

Given that, Speed = 1100 feet per second

and Time = $\dfrac{11}{5}$ sec

We know that,

Distance = Speed * Time

⇒ Distance = $\left(1100 \times \dfrac{11}{5}\right)$ ft

⇒ Distance = 2420 ft

Explanation :

We know that,

Speed = $\dfrac{\text{Distance}}{\text{Time}}$

For first bus :

Let Distance = d₁, time = t₁ and speed = v₁

Here, d₁ = 300 km and t₁ = $\dfrac{15}{2}$ hr

For second bus :

Let Distance = d₂, time = t₂ and speed = v₂

Here, d₂ = 450 km and t₂ = 9 hr

∴ Ratio of speeds = $\dfrac{\text{v}_1}{\text{v}_2}$

= $\dfrac{\text{d}_1}{\text{t}_1}$ : $\dfrac{\text{d}_2}{\text{t}_2}$

= $\left(\dfrac{300}{\dfrac{15}{2}}\right)$ : $\left(\dfrac{450}{9}\right)$

= $\left(300 \times \dfrac{2}{15}\right)$ : $\left(\dfrac{450}{9}\right)$

= 40 : 50

= 4 : 5

Explanation :

We know that,

Speed = $\dfrac{\text{Distance}}{\text{Time}}$

For truck :

Let Distance = d₁, time = t₁ and speed = v₁

Here, d₁ = 550 m and t₁ = 1 min = 60 sec

Then, v₁ = $\dfrac{\text{d}_1}{\text{t}_1}$

⇒ v₁ = $\left(\dfrac{550}{60} \times \dfrac{18}{5} \right)$ km/hr

For bus :

Let Distance = d₂, time = t₂ and speed = v₂

Here, d₂ = 33 km and t₂ = 45 min = $\dfrac{45}{60}$ hr

Then, v₂ = $\dfrac{\text{d}_2}{\text{t}_2}$

⇒ v₂ = $\left(\dfrac{33}{\dfrac{45}{60}}\right)$ km/hr

∴ Ratio of speeds = $\dfrac{\text{v}_1}{\text{v}_2}$

= $\dfrac{\text{d}_1}{\text{t}_1}$ : $\dfrac{\text{d}_2}{\text{t}_2}$

= $\left(\dfrac{550}{60} \times \dfrac{18}{5} \right)$ : $\left(\dfrac{33}{\dfrac{45}{60}}\right)$

= $\left(\dfrac{550}{60} \times \dfrac{18}{5} \right)$ : $\left(\dfrac{33}{45} \times 60 \right)$

= 33 :  44

= 3 : 4

Explanation :

Let the speeds of two trains be 7y and 8y km/hr.

For Second Train :

Let Distance = d₂, Time = t₂ and Speed = v₂

Here, d₂ = 400, t₂ = 4hr, v₂ = 8y

We know that,

Distance = Speed * Time

∴ d₂ = v₂ x t₂

⇒ 400 = 8y x 4

⇒ y = $ \dfrac{400}{4 \times 8} $

⇒ y = 12.5 km/hr

∴ Speed of first train = 7y

⇒ Speed of first train = 7 x 12.5 km/hr

⇒ Speed of first train = 87.5 km/hr

Explanation :

If a car covers a certain distance at a kmph and an equal distance at b kmph.

Then, the average speed of the whole journey = $ \dfrac{2\text{a}\text{b}}{\text{a}+\text{b}}$ kmph

Here, a = 3 kmph, b = 2 kmph

∴ Average speed = $ \dfrac{2 \times 3 \times 2}{3+2}$ = $\dfrac{12}{5}$ km/hr

and, Total time taken = 5 hours

We know that,

Distance = Speed * Time

⇒ Distance = $\left( \dfrac{12}{5} \times 5 \right)$ km

⇒ Distance = 12 km

Hence, Distance between his house and office = $\dfrac{12}{2}$ km = 6 km