Kiran drove from City A to City B, a distance of 242 mi. She increased her speed by 10 mi/h for the 351-mi trip from City B to City C. If the total trip took 12 h, what was her speed from City A to City B?
since time = distance/speed, If she started out with speed x, then
242/x + 351/(x+10) = 12
Yes it is figurative especy the last line
To find Kiran's speed from City A to City B, we can use the formula:
Speed = Distance / Time
Let's denote Kiran's speed from City A to City B as S1 and her speed from City B to City C as S2.
Given information:
Distance from City A to City B = 242 mi
Distance from City B to City C = 351 mi
Total trip time = 12 hours
We know that Kiran's speed from City B to City C is 10 mi/h higher than her speed from City A to City B:
S2 = S1 + 10
Now, let's use the concept of time in our calculations. The time it takes for Kiran to drive from City A to City B can be calculated as:
Time1 = Distance1 / Speed1
Similarly, the time it takes for her to drive from City B to City C can be calculated as:
Time2 = Distance2 / Speed2
Since we know that the total trip took 12 hours, we can write the equation:
Time1 + Time2 = 12
Substituting the values of Time1 and Time2 from the previous equations, we get:
Distance1 / Speed1 + Distance2 / Speed2 = 12
Substituting the given values for Distance1 and Distance2, we have:
242 / Speed1 + 351 / Speed2 = 12
Now, we can substitute the equation S2 = S1 + 10 into the above equation:
242 / Speed1 + 351 / (Speed1 + 10) = 12
To solve this equation, we can cross multiply and simplify:
242(Speed1 + 10) + 351(Speed1) = 12(Speed1)(Speed1 + 10)
Simplifying further:
242Speed1 + 2420 + 351Speed1 = 12Speed1^2 + 120Speed1
Bringing all the terms to one side, we get a quadratic equation:
12Speed1^2 + 120Speed1 - 242Speed1 - 351Speed1 - 2420 = 0
Simplifying:
12Speed1^2 + 7Speed1 - 2420 = 0
Since this is a quadratic equation, we can solve for Speed1 by factoring, using the quadratic formula, or using a calculator. Once we find the value of Speed1, we will have Kiran's speed from City A to City B.