Question

farhan cycles the 1 st part d=150Km at an average speed s=35km/h, and walk the remaining distance at an average speed of 5km/h . if he takes4.5hours for his entire journey, find the distance he cycle. ( the answe is 148 3/4km, how?)

Answer 1

Given :-

$\sf \bullet Total \ Distance (cycle +walk)= 150km\\ \\ \sf\bullet Speed (s_1)[cycle]= 35km/h\\ \\ \sf \bullet Speed (s_2) [walk]=5km/h\\ \\ \sf \bullet Total \ Time =4.5 hours$

To find :-

The distance of 1st part of journey[cycle] $\sf( d_1)$

• As we know that

$\bigstar{\boxed{\sf{Speed=\dfrac{Distance}{Time}}}}$

• First find the Distance of 1st part $\sf( D_1)$

• Put the value of 1st part of journey

$\longmapsto\sf S_1=\dfrac{D_1}{T_1}\\ \\ \longmapsto\sf 35=\dfrac{D_1}{T_1}\\ \\ \longmapsto\sf D_1= 35\times T_1----(i)$

• Now find the time of 2nd part of journey is

$\sf T_2 -T_1 \ \ \longmapsto\sf 4.5-T_1$

• So we have

• $\sf Time [for\ cycling] = (4.5-T_1)\\ \\ \longmapsto\sf S_2= 5km/h\\ \\ \sf D_2=150-D_1$

$\bigstar{\boxed{\sf{Distance= Speed \times Time }}}$

$\longmapsto\sf 150-D_1= 5\times (4.5-T_1)\\ \\ \longmapsto\sf 150-D_1) =22.5-5T_1\\ \\ \longmapsto\sf 150-22.5= - 5T_1+D_1\\ \\ \longmapsto\sf 127.5+5T_1= D_1 \\ \\ \longmapsto\sf or \ \ \ D_1= 127.5+5T_1 ----(ii)$

• From (i) and (ii)

$\longmapsto \sf 127.5+5T_1= 35T_1\\ \\ \longmapsto\sf 127.5= 35T_1-5T_1\\ \\ \longmapsto\sf 127.5= 30T_1\\ \\ \longmapsto\sf T_1=\cancel{\dfrac{127.5}{30}}\\ \\ \longmapsto\sf T_1= 4.25hrs$

Now find the distance of 1st part of journey

put the value of T1 in (i)

$\longmapsto\sf D_1= 35\times T_1\\ \\ \longmapsto\sf D_1= 35\times 4.25\\ \\ \longmapsto\sf D_1= 148.75 \\ \\ \longmapsto\sf or \ \ D_1= \cancel{\dfrac{14875}{100}} = \dfrac{595}{4}\\ \\ \longmapsto\sf D_1= 148\dfrac{3}{4}km$

$\bigstar{\sf{\underline{\dag \ Distance\ he \ cycle =148.75km} }}$

Answer 2

Answer:

Given :

• The total distance (Cycle + Walk) = 150 km.
• The speed of cycling = 35 km/hr.
• Speed of walking = 5 km/hr.
• The total time taken = 4.5 hours.

To Find :

• The distance that he cycle.

Solution :

[ Formula : Speed = Distance/Time ]

Part 1 : 35 = Distance 1 / Time 1

Here, both the quantities ( Distance and Time ) are unknown.

➸ Distance 1 = 35 * Time 1 ..... Equation 1

Part 2 : 5 = Distance 2 / Time 2

Again, both the quantities are unknown here.

➸ Distance 2 = 5 * Time 2

We can also write Distance 2 = 150 - Distance 1.

Also, Time 2 can be written as 4.5 - Time 1.

Hence, equation becomes :

➸ 150 - Distance 1 = 5 * (4.5 - Time 1)

Solving the resultant equation.

➸ 150 - Distance 1 = 22.5 - (5 * Time 1)

➸ (5 * Time 1) - Distance 1 = 22.5 - 150

➸ (5 * Time 1) - Distance 1 = -127.5

➸ -Distance 1 = -127.5 - (5 * Time 1)

➸ Distance 1 = 127.5 + (5 * Time 1)

Now from equation 1.

➸ 35 * Time 1 = 127.5 + (5 * Time 1)

➸ (30 * Time 1) - (5 * Time 1) = 127.5

➸ 30 * Time 1 = 127.5

➸ Time 1 = 127.5/30

➸ Time 1 = 4.25 hrs.

At last, Finding the distance he cycled.

[ Using equation 1 ]

➸ Distance 1 = 35 * Time 1

➸ Distance 1 = 35 * 4.25

➸ Distance 1 = 35 * 4.25

➸ Distance 1 = 148.75 km