Question

A person travels by car from one dty to another with different constant speeds between pairs of cities. She drives for 55.0 min at 65.0 km/h, 16.0 min at 70.0 km/h, and 60.0 min at45.0 km/h and spends 20.0 min eating lunch and buying gas.(a) Determine the average speed for the trip.km/h(b) Determine the distance between the initial and final cities along the routekm

Answer 1

Given,

Time duration to reach the 1st city, t₁=55.0 min

The speed at which the driver drove to 1st city, s₁=65.0 km/h

Time duration to reach the 2nd city, t₂=16.0 min

The speed at which the driver drove to 2nd city, s₂=70 km/hr

Time duration to reach the 3rd city, t₃=60.0 min

The speed at which the driver drove to 3rd city, s₃=45.0 km/hr

The time spent for lunch and buying gas, t₄=20.0 min

The speed of an object is given by,

`s=(d)/(t)`

Thus the distance traveled by the object is given by,

`d=st`

The distance between the 1st pairs of the city is given by

`d_1=s_1t_1`

On substituting the known values,

`\begin{gathered} d_1=65*(55)/(60) \\ =59.58\text{ km} \end{gathered}`

Distance between the second pair of the cities is,

`\begin{gathered} d_2=s_2t_2 \\ =70*(16)/(60) \\ =18.67\text{ km} \end{gathered}`

The distance between the 3rd pair of cities is

`\begin{gathered} d_3=s_3t_3 \\ =45*(60)/(60) \\ =45\text{ km} \end{gathered}`

(a) The average speed is defined as the total distance divided by the total time taken.

Therefore the average speed of the whole trip is calculated as

`s_(av)=(d_1+d_2+d_3)/(t_1+t_2+t_3+t_4)`

On substituting the known values in the above equation,

`\begin{gathered} s_(av)=(59.58+18.67+45)/(((55+16+60+20))/(60)) \\ =(123.25)/(2.52) \\ =48.91\text{ km/hr} \end{gathered}`

Therefore the average speed of the trip is 48.91 km

(b) The distance between the initial and the final cities is given by,

`D=d_1+d_2+d_3`

On substituting the known values in the above equation,

`\begin{gathered} D=59.58+18.67+45 \\ =123.25\text{ km} \end{gathered}`

Therefore the total distance between the initial and the final cities is 123.25 km