Two fireworks are set off simultaneously but from different altitudes. The height y in feet of one is

represented by y=-16t^2+120t+10, where t is the time in seconds. The height of the other is represented by y=-16t^2+60t+310. After how many seconds are the fireworks at the same height? ___________ What is
that height? ______________ i really dont get how to do this someone tell me how

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To find the time at which the fireworks are at the same height, we need to find the value of t when the two equations are equal. Set the two equations equal to each other:

-16t^2 + 120t + 10 = -16t^2 + 60t + 310

By rearranging the equation, we can simplify it:

-16t^2 + 120t + 10 - (-16t^2 + 60t + 310) = 0

Combine like terms:

-16t^2 + 120t + 10 + 16t^2 - 60t - 310 = 0

Simplify further:

60t - 300 = 0

Now, isolate t by moving the constant term to the other side:

60t = 300

And divide both sides by 60:

t = 300 / 60

Simplifying:

t = 5 seconds

Therefore, the fireworks are at the same height after 5 seconds.

To find the height at that time, substitute this value of t into either of the original equations:

For y = -16t^2 + 120t + 10:

y = -16(5)^2 + 120(5) + 10

Simplifying:

y = -16(25) + 600 + 10

y = -400 + 600 + 10

y = 210 ft

So at 5 seconds, both fireworks will be at a height of 210 feet.