Total miles = 70 + 70 = 140 miles
Total time = 140 miles / 57 mph = 2.456 hours
Time 1: 70 miles / 70 mph = 1 hour
Time 2: 70 miles / x mph
Total time = time 1 + time 2:
2.456 = 1 hour + 70/x
Subtract 1 hour from both sides:
1.456 = 70x
multiply both sides by x:
1.456x = 70
Divide both sides by 1.456:
x = 70/1.456
x = 48.0769 miles per hour
Rounded to 2 dp = 48.08 miles per hour
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Answer: 5 and 14.
Step-by-step explanation:
We know that the Raiders and Wildcats both scored the same number of points in the first quarter so let a,a+d,a+2d,a+3d be the quarterly scores for the Wildcats. The sum of the Raiders scores is a(1+r+r^{2}+r^{3}) and the sum of the Wildcats scores is 4a+6d. Now we can narrow our search for the values of a,d, and r. Because points are always measured in positive integers, we can conclude that a and d are positive integers. We can also conclude that $r$ is a positive integer by writing down the equation:
a(1+r+r^{2}+r^{3})=4a+6d+1
Now we can start trying out some values of r. We try r=2, which gives
15a=4a+6d+1
11a=6d+1
We need the smallest multiple of 11 (to satisfy the <100 condition) that is 1 (mod 6). We see that this is 55, and therefore a=5 and d=9.
So the Raiders' first two scores were 5 and 10 and the Wildcats' first two scores were 5 and 14.
The answer is D. The bottom most choice.
