Oscar rode his bicycle at a rate of 9 mph and then speed up to 16 mph. he rode 30 minutes longer at 9 mph than he did at 16 mph. If he traveled a total of 22 miles, how long did he ride at the slower rate?

t = 0.7 h

The time he rode at a slower speed is 1.2 h

Step-by-step explanation:

-The question involves algebra, to find the time the distance formula is used involving the values of distance, time and speed.

- distance = speed 1 * time 1 + speed 2 * time 2

If Oscar traveled for t minutes at 9mph and it took him 15 minutes longer than when he traveled at 16mph it means that:

speed 1 * time 1 + 30 minutes.

But 30 minutes converted to hours is 0.5 hours

22 miles = 9 * (t + 0.5) + 16 * t

22 = 9t + 4.5 + 16t

17.5 = 25t

17.5 / 25 = t

The answer is: t = 0.7

Checking the value in the equation:

22 miles = 9 * (t + 0.5) + 16 * t

22 = 9 * (0.7 + 0.5) + 16 * 0.7

22 = 9 * 1.2 + 11.2

22 = 10.8 + 11.2

22 = 22

42

step-by-step explanation:

256/6=42

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.