Question

Kirk's average driving speed is 7 kilometers per hour faster than Thor's. In the same length of time it takes Kirk to drive 450 kilometers, Thor drives only 408 kilometers. What is Kirk's average speed?

Answer 1

Kirk's average speed is 75 km/h.

Step-by-step explanation:

To find Kirk's average speed, we can use the formula: speed = distance / time.

Let's assume Kirk's average speed is x km/h and Thor's average speed is y km/h. We are given two pieces of information:

Kirk's average driving speed is 7 km/h faster than Thor's speed: x = y + 7

In the same time it takes Kirk to drive 450 km, Thor drives 408 km: 450 / x = 408 / y

We can solve this system of equations to find Kirk's average speed.

1. Begin by solving the first equation for x in terms of y: x = y + 7
2. Substitute this expression for x in the second equation: 450 / (y + 7) = 408 / y
3. Cross-multiply and solve for y: 450y = 408(y + 7)
4. Expand and simplify the equation: 450y = 408y + 2856
5. Subtract 408y from both sides: 42y = 2856
6. Divide by 42: y = 68
7. Substitute this value of y into the first equation to find x: x = 68 + 7 = 75

Therefore, Kirk's average speed is 75 km/h.

Answer 2

x = 816 kilometers per hour.

Step-by-step explanation:

Given the following data;

Distance traveled by Kirk = 450km

Distance traveled by Thor = 408 km

Let the average driving speed of Thor be x.

Translating the word problem into an algebraic equation;

k = x + 6

We know that the time taken to cover a distance by an object with speed is given by the formula;

Time = distance/speed

Substituting into the equation, we have;

408/x = 405/x + 6

Cross-multiplying, we have;

408*(x + 6) = 405*x

408x + 2448 = 405x

408x - 405x = 2448

3x = 2448

x = 2448/3

x = 816 kilometers per hour.