Question

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

Answer 1

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

Answer 2

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