precalculus

please can somebody explain to me how to do this questions

8. Elli travelled 700km by truck to deliver some ostriches to her friend's farm. she then returned the same distance by car. The car averaged 10km/h faster than the truck and took 1 hour less time. What was the speed of the car?

9. When two pumps are turned on they can fill the pond at Cassandra's farm in seven hours. individually, one pump takes two hours longer than the other to fill the pond. Find the time to fill the pond by the faster pump by itself.

10. A boat travelled 30km upstream, against the current, to deliver some feed from Elli, to Helmut's farm, it then turned around and headed 35km downstream to dock for the night. If the speed of the current was 3km/h and the upstream trip took 45 mins longer than the downstream trip, what was the speed of the boat?

this unit is about solving quadratics with the quadratic formula

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  1. If the car's speed was s, then the truck's speed was s-10.
    Since time = distance/speed, and the truck took an extra hour,
    700/(s-10) = 700/s + 1
    clearing the fractions, you get
    700s = 700(s-10) + 1(s)(s-10)
    s^2 - 10s - 7000 = 0
    Now, using the quadratic formula, you have
    s = (10±√(100+28000))/2 = 5±√7025 = 5(1±√281)
    You want the positive value.

    For the pumps, you have the usual work problem, so you have
    1/x + 1/(x+2) = 1/7

    #10 is pretty much like #8. How far do you get on it?

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    oobleck

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