137k views
0 votes
Li Ting travels 700 km by coach from singapore to penang to visit her grandparents. she returns to singapore by car at an average speed which is 30km/h greater than of a coach

User Meir Gabay
by
7.7k points

2 Answers

0 votes
Answer:

2.06 km/h


To solve this problem, we need to use the formula:

distance = speed × time

Let's assume that Li Ting's speed by coach is x km/h. Then, the time taken for her coach journey is:

time by coach = distance / speed = 700 / x hours

Now, let's assume that Li Ting's speed by car is 30 km/h faster than her speed by coach. Therefore, her speed by car is (x + 30) km/h. The time taken for her car journey is:

time by car = distance / speed = 700 / (x + 30) hours

The total time taken for her round trip is the sum of the time taken for her coach journey and the time taken for her car journey:

total time = time by coach + time by car = 700 / x + 700 / (x + 30)

To find Li Ting's average speed for the entire trip, we can use the formula:

average speed = total distance / total time

The total distance of the round trip is 1400 km (700 km each way). Substituting the expressions for the total time and total distance, we get:

average speed = 1400 / (700 / x + 700 / (x + 30))

We can simplify this expression by finding a common denominator:

average speed = 1400 / (700x / x(x + 30) + 700(x + 30) / x(x + 30))
average speed = 1400 / (1400x + 21000) / x(x + 30))
average speed = 1400x(x + 30) / (1400x + 21000)

To find the value of x that maximizes the average speed, we can take the derivative of this expression with respect to x and set it equal to zero:

d/dx [1400x(x + 30) / (1400x + 21000)] = 0
[42000 - 21000x] / (1400x + 21000)^2 = 0
42000 - 21000x = 0
x = 2

Therefore, Li Ting's speed by coach is 2 km/h and her speed by car is 32 km/h. Substituting these values into the expression for the average speed, we get:

average speed = 1400(2)(32) / (1400(2) + 21000)
average speed = 64 / 31
average speed ≈ 2.06 km/h

Therefore, Li Ting's average speed for the entire trip is approximately 2.06 km/h
User Nazra
by
8.6k points
7 votes

Answer:

7.947hrs

Explanation:

Distance one way = 700 km

speed of the car x km/h

Speed of coach = x - 30 km./hr

Time = 700/x + 700/(x - 30) = 20

=> 35/x + 35/(x - 30) = 1

=> 35( x- 30 + x) = x(x - 30)

=> 70x - 1050 = x² - 30x

=> x² - 100x + 1050 = 0

x = (100 ± √100² - 4(1)(1050) )/2

=> x = 88.08 or 11.92 x must be greater than 30

Hence x = 88.08

Speed of car = 88.08 km/hr

time taken for the return journey.​ = 700/88.08 = 7.947 hrs

User Liran Ben Yehuda
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories