Answer:
EF = 58/7
Step-by-step explanation:
If you extend both BC and AD to meet at P you get 3 similar triangles PAB, PEF, and PCD. Let's call BF = 3x and FC = 4x. Therefore the following proportions can be expressed:
BP/7 = (BP+7x)/10
10BP = 7*(BP+7x)
10BP = 7BP+49x
3BP = 49x
BP = (49/3)x
BP/7 = (BP+3x)/EF
EF = (BP+3x)*7/BP
EF = ((49/3)x + 3x)*7/((49/3)x)
EF = ((58/3)x*7*3)/(49x)
EF = 58/7
Answer:
210 miles
Step-by-step explanation:
Let's represent it mathematically.
Ben drove 65 miles more than half the number of miles Steve drove, so we represent it by
B = 65 + ½S
It is also said that together, they drove 500 miles, we represent it with.
B + S = 500
Now, we solve simultaneously.
Let's eliminate the ½ in Ben's drive. So we multiply the equation by 2.
2B = 130 + S.
Rearranging, we have
S = 2B - 130.
We substitute this value of S, in the second equation. So we have.
B + (2B - 130) = 500, open the brackets
B + 2B - 130 = 500
3B - 130 = 500, collecting the like terms
3B = 500 + 130
3B = 630
B = 630/3
B = 210 miles.
Therefore, Ben drove 210 miles.
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All real numbers greater than or equal to -3