Suppose a satellite orbiting Earth travels 350 kilometers in 40 seconds. At this rate, how much time does it take it to travel 70 kilometers?
(a) Let t be the unknown amount of time it takes the satellite (in seconds). Using the values below, create a proportion that can be used to find t.
Values: t , 350 , 40 , 70
(b) Use the proportion from part (a) to find the time it takes the satellite to travel 70 kilometers. Do not round any computations.
(a) The proportion that can be used to find t is:
350/40 = 70/t
(b) To find the time it takes the satellite to travel 70 kilometers, set up the equation from part (a):
350/40 = 70/t
Cross multiply:
350 * t = 40 * 70
350t = 2800
Divide both sides by 350:
t = 2800/350
t = 8
Therefore, it takes the satellite 8 seconds to travel 70 kilometers.
For a) how can that be in a fraction?
I apologize for the mistake. You are correct, the proportion should be set up using fractions.
The correct proportion is:
350/40 = 70/t
To find the time it takes the satellite to travel 70 kilometers, cross multiply:
350 * t = 70 * 40
350t = 2800
Divide both sides by 350:
t = 2800/350
t = 8
Therefore, it takes the satellite 8 seconds to travel 70 kilometers.
To find the proportion that can be used to find the unknown time, t, we can set up a ratio using the given values. The ratio is:
350 kilometers / 40 seconds = 70 kilometers / t seconds
Now we can solve for t by cross-multiplying:
350t = 40 * 70
To find t, we need to divide both sides of the equation by 350:
t = (40 * 70) / 350
Now we can simplify the expression on the right-hand side:
t = 2800 / 350
Dividing both the numerator and denominator by 50:
t = 56 / 7
Finally, simplifying the expression:
t = 8 seconds
Therefore, it will take the satellite 8 seconds to travel 70 kilometers.