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Math  /  Numbers & Operations

Questionand a nearby mountain range. The table gives the altitude (in feet above sea level) for the five checkpoints in the race. Use the table to answer the questions. \begin{tabular}{|c|c|} \hline Checkpoint & (reet ablitude sea level) \\ \hline 1 & 3,225 \\ \hline 2 & -216 \\ \hline 3 & 2,503 \\ \hline 4 & 676 \\ \hline 5 & -95 \\ \hline \end{tabular} (a) How much higher is Checkpoint 4 than Checkpoint 5 ? □\square n higher (b) The top of a hill rises 109 feet above Checkpoint 2. What is the altitude of the top of the hilis? □\square ก

Studdy Solution

STEP 1

1. The altitude of each checkpoint is given in feet above sea level.
2. Differences in altitude can be calculated by direct subtraction.
3. The altitude of the top of a hill can be found by adding the rise in altitude to the altitude at a checkpoint.

STEP 2

1. Determine the difference in altitude between Checkpoint 4 and Checkpoint 5.
2. Calculate the altitude of the top of the hill given the rise above Checkpoint 2.

STEP 3

Identify the altitudes of Checkpoints 4 and 5 from the table. Altitude at Checkpoint 4=676 feet\text{Altitude at Checkpoint 4} = 676 \text{ feet} Altitude at Checkpoint 5=−95 feet\text{Altitude at Checkpoint 5} = -95 \text{ feet}

STEP 4

Calculate the difference in altitude between Checkpoint 4 and Checkpoint 5. Difference=Altitude at Checkpoint 4−Altitude at Checkpoint 5\text{Difference} = \text{Altitude at Checkpoint 4} - \text{Altitude at Checkpoint 5} Difference=676−(−95)\text{Difference} = 676 - (-95) Difference=676+95=771 feet\text{Difference} = 676 + 95 = 771 \text{ feet}

STEP 5

Identify the altitude of Checkpoint 2 and the rise in altitude to the top of the hill. Altitude at Checkpoint 2=−216 feet\text{Altitude at Checkpoint 2} = -216 \text{ feet} Rise in altitude=109 feet\text{Rise in altitude} = 109 \text{ feet}

STEP 6

Calculate the altitude of the top of the hill by adding the rise to the altitude at Checkpoint 2. Altitude of the top of the hill=Altitude at Checkpoint 2+Rise in altitude\text{Altitude of the top of the hill} = \text{Altitude at Checkpoint 2} + \text{Rise in altitude} Altitude of the top of the hill=−216+109\text{Altitude of the top of the hill} = -216 + 109 Altitude of the top of the hill=−107 feet\text{Altitude of the top of the hill} = -107 \text{ feet}
Solution: (a) The difference in altitude between Checkpoint 4 and Checkpoint 5 is 771 feet771 \text{ feet}.
(b) The altitude of the top of the hill is −107 feet-107 \text{ feet}.

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