Question

Lorry à and b moving to a townew is 300km apart. Lorry a moves 50 km faster. Lorry b leaves 1 hr prior. They arrive at the same time. Determine their speeds

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, Speed of Lorry b is x km/h.

Than,

→ Speed of Lorry a = (x + 50)km/h.

Now,

→ Distance covered = 300km

→ speed of Lorry b = x km/h.

→ Time taken by him to reach new town = (Distance)/(speed) = (300/x) Hours.

Similarly,

→ Distance covered = 300km

→ speed of Lorry a = (x+50) km/h.

→ Time taken by him to reach new town = (Distance)/(speed) = 300/(x+50) Hours.

Now, we have given that, Lorry b leaves 1 hr prior . That means , he travelled for 1 hr more . and as they reach the destination at same time , we can say that, difference b/w their time is 1 hour.

Therefore,

→ (300/x) - 300/(x + 50) = 1

→ 300[1/x - 1/(x + 50)] = 1

→ (x + 50 - x)/x(x+50) = 1/300

→ x² + 50x = 50*300

→ x² + 50x - 15000 = 0

→ x² + 150x - 100x - 15000 = 0

→ x(x + 150) - 100(x + 150) = 0

→ (x + 150)(x - 100) = 0

→ x = (-150) or 100 .

Since speed in -ve is not Possible.

Hence,

→ Speed of Lorry b = 100km/h. (Ans.)

→ Speed of Lorry a = 150km/h. (Ans.)

[ Nice Ques. ]

Answer 2

GIVEN:

• Lorry 'b' is 50 km faster than Lorry 'a'
• Total Distance covered by Lorry 'a' and 'b' = 300 km

TO FIND:

• What is the speed of Lorry 'a' and Lorry 'b' ?

SOLUTION:

Let the speed of Lorry 'b' be 'p' km/hr

☞ We have given that, Lorry 'b' is 50 km faster than Lorry 'a'

Speed of Lorry 'a' be (p + 50) km/hr

We know that the formula for finding the time taken is:-

$\bf{\star \: Time = \dfrac{Distance}{Speed}\: \star}$

◇ Time taken by the Lorry 'b' = $\bf{\dfrac{ 300}{p} \: hr}$

◇ Time taken by the Lorry 'a' = $\bf{\dfrac{ 300}{p + 50} \: hr}$

In this case, Lorry b taken 1 hour more than Lorry 'a'

According to question:-

$\rm{\dashrightarrow \dfrac{300}{p} - \dfrac{300}{p+50} = 1 }$

$\rm{\dashrightarrow \dfrac{300(p + 50) - 300p}{p(p + 50)} = 1 }$

$\rm{\dashrightarrow \dfrac{300p + 15000 - 300p}{p^2 + 50p} = 1 }$

$\rm{\dashrightarrow 15000 = p^2 + 50p }$

$\rm{\dashrightarrow 0 = p^2 + 50p - 15000}$

$\rm{\dashrightarrow 0 = p^2 +(150-100)p -15000 }$

$\rm{\dashrightarrow 0 = p^2 + 150p - 100p - 15000 }$

$\rm{\dashrightarrow 0 = p(p + 150) - 100(p + 150) }$

$\rm{\dashrightarrow (p+150)(p-100)=0 }$

$\bf{\dashrightarrow p = - 150 km/hr }$(Speed can't be in negative)

$\bf{\dashrightarrow p = 100 km/hr }$

• Lorry b's speed = 100 km/hr
• Lorry a's speed = (100 + 50) = 150 km/hr

❝ Hence, the speeds of Lorry 'a' and 'b' are 150 km/hr and 100 km/hr respectively ❞

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